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Behavioral and RT-level estimation and optimization of crosstalk in VLSI ASICs

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Behavioral and RT-level estimation and optimization of crosstalk in VLSI ASICs
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Gupta, Suvodeep
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Subjects / Keywords:
word-level statistics
probability
floorplanner
routing
synthesis
Dissertations, Academic -- Computer Science and Engineering -- Doctoral -- USF   ( lcsh )
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
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Summary:
ABSTRACT: Signal integrity is a very critical parameter in modern digital circuits. The downscaling of technologies to enable miniaturization results in loss of signal integrity on account of crosstalk between interconnect signal lines placed very close to one another. There arises an acute need of methodologies to estimate crosstalk in interconnects and minimize it, in order to generate reliable designs. Although there exist several crosstalk estimation and optimization techniques in literature, most of these techniques operate at the layout-level of circuits. There is a dearth of techniques which tackle the crosstalk estimation and optimization problem at the behavioral and RT-levels where the design-space can be explored more efficiently, compared to the layout-level. We try to fill this void by proposing word-level statistical techniques which estimate crosstalk between different bus lines.We then integrate the high-level estimators with a place and route tool to estimate crosstalk between different buses at the layout level of designs. Further, we propose a register binding technique during high-level synthesis to minimize register crosstalk activity in the RT-level designs. Specifics related to each proposed technique are presented below. We address the intra-bus crosstalk estimation problem by presenting two high-level techniques to estimate the probability of crosstalk within the lines of a system bus: (1) Given an input data stream, the first technique simply estimates the number of crosstalk events on each line of the bus. The main drawback of this technique is that the execution time is proportional to the stream length. This is overcome by the second enumerative technique which is purely statistical in nature.(2) Given the word-level statistical parameters, namely mean, standard deviation, and lag-one temporal correlation coefficient, we estimate the bit-level crosstalk probability. Experimental results for data streams from different data environments, compared against detailed HSPICE simulations, are presented. There is an exact match between (1) and the corresponding HSPICE simulations while (2) has less than 7% average error, compared to HSPICE. The estimation time of (2) is significantly less than (1) as well as the HSPICE simulations. However, this enumerative technique still suffers from exponential complexity with respect to the bus-width. In order to speedup the statistical enumerative method, we then propose a statistical non-enumerative technique that has linear time complexity with respect to the bus-width.We achieve the linear complexity by resorting to: (1) manipulation of the data stream to make the crosstalk-producing values continuous; and (2) sampling the distribution function and storing it as a lookup table. Experimental results for data streams from different data environments are presented, compared against the stream-based approach. Average errors of less than 15% are obtained for bus-widths ranging from 8b to 32b. The estimation time is reduced by over two orders of magnitude, compared to HSPICE. The statistical approaches are shown to be compatible with existing bus re-ordering techniques. Thus, we are able to estimate the crosstalk susceptibility of lines within a bus very efficiently. We then address the problem of estimating crosstalk between different buses at the layout-level of designs. We propose a technique to measure the crosstalk susceptibility of different nets in the post global routing phase, prior to detailed routing of designs.Global routing provides the approximate routes of the wires. This is used to compute the aggressors of a given victim wire along its route and its crosstalk susceptibility with respect to those aggressors. The crosstalk susceptibility of a wire is given by (1) P(t), the probability of crosstalk occurrence on the wire in different regions along its route; and (2) V(peak), the worst case crosstalk noise amplitude experienced by the wire along its route. P(t) is estimated using the fast and accurate statistical estimator we previously proposed. V(peak) is estimated by predicting the cross-coupling capacitances between neighboring wires, using their global routing information. Placement and global routing are done using CADENCE Silicon Ensemble. The predicted crosstalk estimates are compared against detailed HSPICE simulations. Average errors are found to be less than 8%.We modify the estimation technique, using a root mean square cost function, to obtain single values for the crosstalk probability and noise amplitude of a victim wire along its entire route by combining the values from individual regions through which it passes. Further, we propose a register binding technique during high-level synthesis to minimize crosstalk at the register outputs in the RT-level design. The technique involves modification of the clique-partitioning algorithm to make crosstalk-aware choices of edges to be mapped to the same register. RT-level comparisons between the regular and crosstalk-aware designs show upto 16% reduction in crosstalk activity at the register outputs.
Thesis:
Thesis (Ph.D.)--University of South Florida, 2004.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
Statement of Responsibility:
by Suvodeep Gupta.
General Note:
Includes vita.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 132 pages.

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oclc - 57715178
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usfldc doi - E14-SFE0000513
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ABSTRACT: Signal integrity is a very critical parameter in modern digital circuits. The downscaling of technologies to enable miniaturization results in loss of signal integrity on account of crosstalk between interconnect signal lines placed very close to one another. There arises an acute need of methodologies to estimate crosstalk in interconnects and minimize it, in order to generate reliable designs. Although there exist several crosstalk estimation and optimization techniques in literature, most of these techniques operate at the layout-level of circuits. There is a dearth of techniques which tackle the crosstalk estimation and optimization problem at the behavioral and RT-levels where the design-space can be explored more efficiently, compared to the layout-level. We try to fill this void by proposing word-level statistical techniques which estimate crosstalk between different bus lines.We then integrate the high-level estimators with a place and route tool to estimate crosstalk between different buses at the layout level of designs. Further, we propose a register binding technique during high-level synthesis to minimize register crosstalk activity in the RT-level designs. Specifics related to each proposed technique are presented below. We address the intra-bus crosstalk estimation problem by presenting two high-level techniques to estimate the probability of crosstalk within the lines of a system bus: (1) Given an input data stream, the first technique simply estimates the number of crosstalk events on each line of the bus. The main drawback of this technique is that the execution time is proportional to the stream length. This is overcome by the second enumerative technique which is purely statistical in nature.(2) Given the word-level statistical parameters, namely mean, standard deviation, and lag-one temporal correlation coefficient, we estimate the bit-level crosstalk probability. Experimental results for data streams from different data environments, compared against detailed HSPICE simulations, are presented. There is an exact match between (1) and the corresponding HSPICE simulations while (2) has less than 7% average error, compared to HSPICE. The estimation time of (2) is significantly less than (1) as well as the HSPICE simulations. However, this enumerative technique still suffers from exponential complexity with respect to the bus-width. In order to speedup the statistical enumerative method, we then propose a statistical non-enumerative technique that has linear time complexity with respect to the bus-width.We achieve the linear complexity by resorting to: (1) manipulation of the data stream to make the crosstalk-producing values continuous; and (2) sampling the distribution function and storing it as a lookup table. Experimental results for data streams from different data environments are presented, compared against the stream-based approach. Average errors of less than 15% are obtained for bus-widths ranging from 8b to 32b. The estimation time is reduced by over two orders of magnitude, compared to HSPICE. The statistical approaches are shown to be compatible with existing bus re-ordering techniques. Thus, we are able to estimate the crosstalk susceptibility of lines within a bus very efficiently. We then address the problem of estimating crosstalk between different buses at the layout-level of designs. We propose a technique to measure the crosstalk susceptibility of different nets in the post global routing phase, prior to detailed routing of designs.Global routing provides the approximate routes of the wires. This is used to compute the aggressors of a given victim wire along its route and its crosstalk susceptibility with respect to those aggressors. The crosstalk susceptibility of a wire is given by (1) P(t), the probability of crosstalk occurrence on the wire in different regions along its route; and (2) V(peak), the worst case crosstalk noise amplitude experienced by the wire along its route. P(t) is estimated using the fast and accurate statistical estimator we previously proposed. V(peak) is estimated by predicting the cross-coupling capacitances between neighboring wires, using their global routing information. Placement and global routing are done using CADENCE Silicon Ensemble. The predicted crosstalk estimates are compared against detailed HSPICE simulations. Average errors are found to be less than 8%.We modify the estimation technique, using a root mean square cost function, to obtain single values for the crosstalk probability and noise amplitude of a victim wire along its entire route by combining the values from individual regions through which it passes. Further, we propose a register binding technique during high-level synthesis to minimize crosstalk at the register outputs in the RT-level design. The technique involves modification of the clique-partitioning algorithm to make crosstalk-aware choices of edges to be mapped to the same register. RT-level comparisons between the regular and crosstalk-aware designs show upto 16% reduction in crosstalk activity at the register outputs.
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BehavioralandRT-LevelEstimationandOptimizationofCro sstalkinVLSIASICs by SuvodeepGupta Adissertationsubmittedinpartialfulllment oftherequirementsforthedegreeof DoctorofPhilosophy DepartmentofComputerScienceandEngineering CollegeofEngineering UniversityofSouthFlorida MajorProfessor:SrinivasKatkoori,Ph.D. NagarajanRanganathan,Ph.D. HaoZheng,Ph.D. WilfridoMoreno,Ph.D. A.N.V.Rao,Ph.D. DateofApproval:November1,2004 Keywords:word-levelstatistics,probability,roorplann er,routing,synthesis c r Copyright2004,SuvodeepGupta

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DEDICATION Tomyfamilyandallotherswhoinspiredmetoperseverethrou ghtryingtimes.

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ACKNOWLEDGEMENTS IwouldliketothankDr.Katkooriimmenselyforhisguidance ,encouragement,and patienceduringtheentirecourseofthisresearch.Iwouldl iketothankDr.Ranganathan, Dr.Zheng,Dr.Moreno,andDr.Raoforbeingonmycommittee.I takethisopportunity toacknowledgetheintellectualandmoralsupportprovided bycurrentandpastmembers oftheVCAPPgroup,especiallyChandramouli,Stelian,Hao, Saraju,andAnanth.Iwould liketoacknowledgethehelpprovidedbytheComputerScienc eTechSupportteamledby DanielPrieto.Mostimportantly,Iwouldliketothankmyfam ilyformakingmebelieve inmyselfbesidesmuchmore.Finally,abigthankyoutomyfri endsforbeingthereforme throughoutthisroller-coasterride.

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TABLEOFCONTENTS LISTOFTABLES iii LISTOFFIGURES v ABSTRACT viii CHAPTER1INTRODUCTION 1 1.1Bus-basedinterconnects 6 1.2ASICdesignrow 8 1.3High-levelestimation:anadvantage 9 1.4Proposedapproachtothecrosstalkestimationproblem1 1 1.4.1Intra-buscrosstalkestimation121.4.2Inter-buscrosstalkestimation13 1.5Optimizationforcrosstalk 14 1.6Organization 14 CHAPTER2BACKGROUNDANDRELATEDWORK16 2.1Layout-levelcrosstalkestimation 16 2.2Gate-levelcrosstalkestimation 19 2.3High-levelestimationofcircuitparameters22 2.3.1Worst-casecrosstalkmetrics 25 2.4Crosstalkoptimization 27 2.4.1Shielding 27 2.4.2Wirereordering 27 2.4.3Busencoding 28 2.5Word-levelstatisticalestimators 30 2.6Dataenvironments 34 2.7Summary 35 CHAPTER3INTRA-BUSCROSSTALKESTIMATIONUSINGWORD-LEVEL STATISTICS 37 3.1Modelingthecrosstalkestimationproblem373.2Problemformulation 38 3.3Proposedtechnique1:stream-basedcrosstalkeventest imator41 3.4Proposedtechnique2:statisticalenumerativeapproac hforcrosstalk eventestimation 43 3.4.1Crosstalkformiddlelines 47 3.4.2Crosstalkforedgelines 49 i

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3.5Experimentalresults 50 3.6Conclusions 53 CHAPTER4IMPROVINGTHECOMPLEXITYOFTHESTATISTICALESTIMATION 54 4.1Introductionandproblemformulation 54 4.2Proposedstatisticalnon-enumerativeapproach55 4.2.1Evaluationofthedeniteintegralusingsampling58 4.3Experimentalresults 60 4.4Conclusions 65 CHAPTER5FLOORPLAN-BASEDCROSSTALKESTIMATIONFORMACROCELLBASEDDESIGNS 68 5.1Thesignicanceoftheinter-buscrosstalkproblem685.2Theplaceandroutetool 71 5.3Modelingtheinter-wirecrosstalkproblem74 5.3.1Validatingtheempiricalwire-orderingassumptions 74 5.3.2RT-levelproling 75 5.3.3Compositebusformation 76 5.4Estimatingtheinter-wirecrosstalkmetrics77 5.4.1Crosstalkprobabilityestimation775.4.2Maximumnoisepulseestimation785.4.3Modicationoftheestimationprocessusinguniformwiremodels-rmsestimate 80 5.5Experimentalresults 82 5.5.1RCmodels 82 5.6Conclusions 88 CHAPTER6BINDINGFORCROSSTALKMINIMIZATIONDURINGHIGHLE VEL SYNTHESIS 92 6.1The au tomatic d esign i nstantiation( audi )synthesissystem92 6.2Crosstalkcharacterizationofdesigns 96 6.3Bindingduringhigh-levelsynthesis 97 6.3.1Cliquepartitioning 102 6.4Experimentalrowandresults 103 6.5Conclusions 108 CHAPTER7CONCLUSIONSANDFUTUREWORK109REFERENCES 112 ABOUTTHEAUTHOR EndPage ii

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LISTOFTABLES Table1.1Projectedpowertrends(ITRS2003) 3 Table2.1Couplingcapacitanceoftwowiresfordierentove rlapping lengths(reproducedfromTienet.al.[1])20 Table2.2Crosstalknoiseofthevictimproductlinefordie rentproduct lines(reproducedfromTienet.al.[21])20 Table3.1Possiblecrosstalkeects 39 Table3.2HSPICEvsstream-basedruntimes 43 Table3.3Dataenvironments 50 Table3.4Crosstalkprobabilityfor8-bitbus-SIG1andSIG2 51 Table3.5Crosstalkprobabilityfor8-bitbus-SIG3andSIG4 51 Table3.6Crosstalkprobabilityfor10-bitbus-SIG1andSIG 252 Table3.7Stream-basedestimatorvsstatisticalenumerato rruntimes52 Table4.1Dataenvironments 60 Table4.2Crosstalkprobabilityfor8-bitbus 61 Table4.3Crosstalkprobabilityfor8-bitbus-SIG1&realau diodata62 Table4.4Crosstalkprobabilityfor16-bitbus 63 Table4.5Crosstalkprobabilityfor32-bitbus 64 Table4.6Stream-basedestimatorvsstatisticalestimator runtimes64 Table4.7Eectofsamples(s)onruntimes 65 Table4.8Avg.crosstalkestimationerror-FIR66Table4.9Crosstalkprobabilitiesonoriginalandre-order edbuslinesand decreaseincrosstalksusceptibilityduetore-ordering66 Table4.10Estimationprobabilitiesfororiginalandre-or deredbus66 iii

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Table5.1Wire-orderingvalidation 75 Table5.2Benchmarkdetails 84 Table5.3Crosstalkprobabilityestimationerrorscompare dtoHSPICE84 Table5.4Executiontimesofcrosstalkprobabilityestimat ion85 Table5.5Amplitudeestimatesagainstsimulatedvaluesfor dierentgcells85 Table5.6Crosstalksusceptibilitydistributionofvictim nets(0.00-0.40)87 Table5.7Crosstalksusceptibilitydistributionofvictim nets(0.41-0.70)87 Table5.8ErrorbinsofestimationerrorswrtHSPICE(unifor mwiremodels)88 Table5.9EstimationerrorstatisticscomparedtoHSPICE(u niformwiremodels)88 Table5.10Averageexecutiontimesofestimationcomparedt osimulation (eachvictimwire) 88 Table6.1DetailsofDiEqdatapath 97 Table6.2DiEqdatapathcharacterization-asap97Table6.3DiEqdatapathcharacterization-alap/fds98Table6.4DetailsofFIRdatapath 98 Table6.5FIRdatapathcharacterization-asap 98 Table6.6FIRdatapathcharacterization-alap/fds98Table6.7DetailsofIIRdatapath 99 Table6.8IIRdatapathcharacterization-asap 99 Table6.9IIRdatapathcharacterization-alap/fds99Table6.10Crosstalkreductionduetocrosstalk-awarebind ing(asapscheduling)-DiEq 106 Table6.11Crosstalkreductionduetocrosstalk-awarebind ing(asapscheduling)-FIRlter 106 Table6.12Crosstalkreductionduetocrosstalk-awarebind ing(alapscheduling)-IIRlter 107 Table6.13Comparionofruntimes 107 Table6.14Comparionofresourceusage 107 iv

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LISTOFFIGURES Figure1.1Scalingdownoftechnologynodes(ITRS2003)2Figure1.2Subcircuitwithwire-to-substratecapacitance s4 Figure1.3Twosub-circuitsincloseproximity 4 Figure1.4Cross-couplingcapacitanceasadominantfactor innanometer technology(ReproducedfromKimet.al.[2])5 Figure1.5Interactionbetweendesignandtestphasestoeli minatecouplingfaults 6 Figure1.6Thevariouscapacitancesinadesign 7 Figure1.7Top-downdesignrow 9 Figure1.8RT-leveltogatel-levelusinglogicsynthesis10Figure1.9Aggressor-victimsimulationcircuit 13 Figure2.1Equivalentcircuitforcomputingcrosstalknois eamplitude18 Figure2.2AnexampleofaPLA(originalconguration)21Figure2.3Reductioninwirelengthusingreordering21Figure2.4Bell-shapedcurveofentropyforbooleanvariabl es25 Figure2.5Shieldingwireinputvictimandaggressor28Figure2.6Eliminatingcrosstalkbybusreordering28Figure2.7Communicationchainmodel 29 Figure2.8Eliminatingdelaywithself-shieldingcodes29Figure2.9Dierentregionsinadatawordbasedontransitio nactivity31 Figure2.10Capacitivecoecientsfordierentsign-bittr ansitions32 Figure2.11Statisticspropagationinanadder 33 v

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Figure3.1Crosstalkspikeeectsonvictims 39 Figure3.2Crosstalkdelayeectsinvictims 40 Figure3.3Aggressor-victimsimulationcircuit 42 Figure3.4Checkingbittransitionsforcrosstalkpatterns 42 Figure3.5Concatenation 46 Figure3.6Bit-levelcrosstalktemplatesfor8-bitbus48Figure3.7Proceduralrow 49 Figure4.1Concatenation 55 Figure4.2Continuouscrosstalkwindowsusingcircularrig htshift56 Figure4.3Enumerative&non-enumerativetechniquesfora4 -bitbus withtemplateinstance000011andvictimb158 Figure4.4Enumerationtointegraltransformation59Figure4.5Thesamplingtechnique 60 Figure4.6Non-enumerativestatisticalcrosstalkprobabi lityestimationrow61 Figure4.7FIRlter 63 Figure5.1Globalroutingofwires 72 Figure5.2Horizontalorderingofwiresduringglobalrouti ng73 Figure5.3Vericalorderingofwiresduringglobalrouting7 3 Figure5.4Generalprocedurerow 74 Figure5.5Formationofthecompositebusfromglobalroute7 6 Figure5.6Cross-couplinginparallelwires 78 Figure5.7Experimentalrow 81 Figure5.8TheRCmodelforeverygcell 83 Figure5.9Experimentalrow(uniformwiremodel)86Figure5.10AmplitudesimulationinHSPICE-2-wiremodel89Figure5.11AmplitudesimulationinHSPICE-4-wiremodel90Figure6.1Asap/alapschedulesforadatarowgraph101 vi

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Figure6.2Cliquepartitioningexample 103 Figure6.3Cliquepartitioningforcrosstalkminimization 104 Figure6.4Experimentalrowforrtlcrosstalkoptimization 105 vii

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BEHAVIORALANDRT-LEVELESTIMATIONANDOPTIMIZATIONOF CROSSTALKINVLSIASICS SuvodeepGupta ABSTRACT Downscalingoftechnologycausessignalintegrityproblem sduetocrosstalkbetween closely-spacedinterconnectlines.Existingcrosstalkes timationandoptimizationtechniques operateatthelayout-levelofcircuitsandfailtoutilizet heecientdesign-spaceexploration atthehigh-level.Toaddressthis,weproposeword-levelst atisticaltechniqueswhichestimatecrosstalkbetweenbuslines:(1)Givenadatastream,th ersttechniquesimplycounts thenumberofcrosstalkeventsoneachbusline.Thedrawback ofthistechniqueisthat theexecutiontimeisproportionaltothestreamlength.Thi sisovercomebythesecond enumerative techniquewhichispurelystatisticalinnature.(2)Givenw ord-levelstatistics, weestimatethebit-levelcrosstalkprobabilityofbusline s.(3)Wefurtherspeedupthe statisticalmethodusinga non-enumerative techniquebylinearizingitscomplexitywithrespecttothebuswidth.Averageerrorsoflessthan15%areobt ainedforbus-widthsranging from8bto32bwhileexecutiontimesarereducedbytwoorders ofmagnitude,comparedto HSPICE. Wethenmeasurethecrosstalksusceptibilityofnetsinthep ostglobalroutingphase (performedusingCADENCESiliconEnsemble),priortodetai ledroutingusing(1) P t ,the probabilityofcrosstalkonvictimsindierentregionsalo ngtheirroute;and(2) V peak themaximumcrosstalknoiseamplitudeexperiencedbyvicti msalongtheirroute. P t is estimatedusingthefastandaccuratestatisticalestimato rwepreviouslyproposed. V peak is estimatedbypredictingthecross-couplingcapacitancesb etweenneighboringwires,using theirglobalroutinginformation.Averageerrorsarelesst han8%,comparedtoHSPICE. viii

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Wecombinethecrosstalksusceptibilityvaluesfromindivi dualregionsalongavictimwire's route,toobtainasinglesusceptibilityvaluefortheentir ewire. Further,weproposearegisterbindingtechniqueduringhig h-levelsynthesistominimize crosstalkattheregisteroutputsintheRT-leveldesign.It involvesmodicationofthecliquepartitioningalgorithmtomakecrosstalk-awarechoicesof edgestobemappedtothesame register.RT-levelcomparisonsbetweentheregularandcro sstalk-awaredesignsshowupto 16%reductionincrosstalkactivityattheregisteroutputs ix

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CHAPTER1 INTRODUCTION ThelastfourdecadeshaveseentherealmofVLSIdesignexpan databreathtaking pace.Startingwiththe microprocessorrevolution inthesixties,thedigitalcircuitdomain haswitnessedunprecedentedchangesinbothtechnologyand designstyle.Thecircuit componentshaveshrunkinsizewhilethetotalnumberofcomp onentswithinaxedchip areahasincreasedmanifold,inaccordancewiththeempiric ally-predictedMoore'slaw.The combinedeectofthesefactorshasresultedinscalingdown oftechnologyintotheverydeep-submicron(VDSM)andultra-deepsubmicron(UDSM)reg imeswherethephysical distancebetweendierentcomponentshasbecomeextremely small. Existingtechnologyenhancementshaveincreasedcircuits peedandcomplexitywhile simultaneouslyincreasingpowerconsumptionandshrinkin garea.However,attheVDSM andUDSMtechnologyregimes,designersarenowfacedwithne wchallenges.Theinteractionbetweenthecircuitcomponentshasbecomesigni cantlydierentcomparedto previoustechnologiesandhasgivenrisetoneweectssucha scoupling,IRdrop,electromigration,andleakagepowerdissipation.Theseeects,wh ichwereinconsequentialbefore, havebecomecriticaldesignparameterswithimmenseeects onthefunctionalityandreliabilityofthecircuit.Asaresult,techniquestoestimat eandoptimizetheseeectshave becomeincreasinglyimportantresearchareas.Itispredic tedthattheseeectswillnotonly altertheconventionaldesignrowbutwillevenchangetheex istingdevicestructuresinthe foreseeablefuture[3]. Further,theworld-widedemandforsmallerandmoreportabl edeviceshasbeenincreasingatarapidpace.Thisiscorroboratedbytherisingsaleso fPDAsandpalmtopsinthe commercialmarket.Inordertokeepupwiththerisingdemand softhemarket,newand 1

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0.01 1.0 10 0.1Feature size (Half Pitch) (microns)ITRS Technology nodes Worldwide wafer production capacity YEAR2003 2002 2001 2000 1999 1998 1997 n n n n r r r r r r r r r r r r Figure1.1.Scalingdownoftechnologynodes(ITRS2003) improvedtechniquesforextensiveminiaturizationofcirc uitsiscalledfor.Figure1.1indicatesthescalingdownoftechnologynodesincircuitsaswel lastheworldwideproduction ofcircuitsbelongingtovariousfeaturesizes,asprojecte dbytheInternationalTechnologyRoadmapforSemiconductors(ITRS)2003[3].Theguresh owsthatthetechnology sizehasbeenconstantlydecreasingovertheyears.Besides ,theworld-wideproductionof end-productswithlargertargettechnologiesisalsodimin ishing.Miniaturizationofcircuits causesreliabilitytobecomeanissueofconcern.Ononehand ,noisesensitivityofthese circuitsshouldbekeptataminimuminordertopreservereli ability.Atthesametime, dynamicpowerconsumptioninthesedevicesmustbekeptatam inimuminordertoenhancetheirlifetimes.Weanalyzetheeectsofchangesinth esupplyvoltageonthesetwo designconsiderations.Equation1.1showsthequadraticde pendenceofthedynamicpower onthesupplyvoltageofthecircuits.Thus,theoperatingvo ltagemustbedecreasedin ordertorestrictthedynamicpowerconsumptioninthecircu it.AccordingtoITRS03,the operatingvoltagedecreasesabout20%pertechnologynodei nordertokeepthedynamic powerconsumptionofthecircuitsincheck.Table1.1showst heprojectedpowertrends overthenextveyears.Itcanbeseenthatalthoughthesuppl yvoltagewilldecrease, 2

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Table1.1.Projectedpowertrends(ITRS2003) Performancefactor 2004 2005 2006 2007 2008 Supplyvoltage(V) 0.9 0.9 0.9 0.8 0.8 Powerconsumption(W) 158 167 180 189 200 Batterypower(W) 2.2 2.3 2.4 2.5 2.6 thetotalpowerconsumptioninthecircuitwillcontinuetoi ncrease.Thisisbecausethe increasingnumberofcomponentswithinaxedchipareawill giverisetoincreasingcomponentdensities.Thepowerconsumptioninthebatterieswh ichpowerthesedeviceswill correspondinglyincrease. P cap = C L E ( sw ) V 2 DD f (1.1) where C L isthelumpednodecapacitance, E ( sw )istheswitchingactivityatthenode, V DD isthesupplyvoltage,and f istheclockfrequency.However,thedecreasingsupply voltageswillhaveadverseeectsonboththedelayaswellas thenoisesensitivityofthe circuits.Equation1.2showstheinverserelationbetweent hesupplyvoltage V DD andcircuit delay t D t D = C L 2 V DD k 1 p + k 2 n (1.2) where p and n arethegainfactorsofthe p and n transistorsrespectively. k 1 and k 2 takevalues1.5and2forvaluesof V DD between3and5volts.Whiletheincreasing delaycanbeosettosomeextentbyloweringthethresholdvo ltageofthetransistors, thedecreasingthresholdvoltageincreasesthenoisesensi tivityofthecircuit.Thenoise sourcesaretypicallyspreadwidelyoverthechip.Themajor noisesourceamongtheseis the interconnectnoise .Thiswillbeanalyzedindetail. Theenormousnumberofcomponentsalongwithsmalldevicefe aturesincreasesthe proximitybetweenthedierentcomponentsofthedesign.Ea chindividualcomponent givesrisetoacapacitancerelativetothesubstrate.Thisi sknownasthe wire-to-substrate 3

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SUBCKTCCg1gnInputsLL 1 n Figure1.2.Subcircuitwithwire-to-substratecapacitanc esGND GND GNDGND GND GND SUBCKT 2 SUBCKT 1 g11InputsInputsx x xCC Cg2n g22 g21 g1n g1n'C C C C C C Figure1.3.Twosub-circuitsincloseproximity capacitance .Forexample,inFigure1.2,eachoutputlineoftheCMOSsubc ircuithasa capacitance C g ,relativetotheground.Thus, n -outputlineshavewire-to-substratecapacitances C g 1 through C gn Ontheotherhand,acapacitance C x mayexistbetween Closely-locatedwiresofacommonsubcircuit. Closely-locatedwiresofdierentsubcircuitswhicharein thevicinityofoneanother. Suchacapacitanceisknownasthe cross-coupling capacitance.BothtypesofcrosscouplingcapacitancesareshowninFigure1.3.Ifthewire-t o-substratecapacitance C g is muchhigherthanthecross-couplingcapacitance C x ,theneachlinehasahighdrivestrength anddierentlinesdonotinruenceeachotherinanyway.Howe ver,atlowertechnology regimes,thethicknessofthemetalisincreased,withrespe cttothespacingbetweenthe 4

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40 50 60 70 80 90 5 x Min spacing 2 x Min spacing Min spacing 0 25018070 100 130 150C x C total x 100Process (nm) 30 10 20Figure1.4.Cross-couplingcapacitanceasadominantfacto rinnanometertechnology(ReproducedfromKimet.al.[2])lines,inordertomaintainalowresistanceforthelines[4] .Theratioofthecross-coupling capacitancetothewire-to-substratecapacitancecouldbe ashighas3:1.Asaresult, thecross-couplingcapacitancebecomessignicantascomp aredtothewire-to-substrate capacitance.Thus,previouslyunrelatedeventssuchastra nsitionsontwoclosely-located lines,begintoinruenceoneanother.Thisphenomenoniskno wnas crosstalk andishighly undesirableindigitalcircuits,sincetheyhaveadversee ectsonboththedelayandthe powerconsumptioninthecircuit,leadingtosignalintegri tyandreliabilityfailures.This willcausethecircuittomalfunctioncompletelyorworsest ill,functionintermittently[4]. Figure1.4showstheprojecteddominanceofcross-coupling capacitancewithrespecttothe totalwirecapacitancewiththescalingdownoftechnologyn odes[2]. Theadverseeectsofcrosstalkarefeltnotonlyinthedesig neldbutinthetesteld aswell.Duetoincreasinginteractionbetweendesignersan dtestersandtheadventofthe designfortestability concept,designersneedtoaccountforcross-couplingfaul tsthatmay surfaceduringthetestingprocessofacircuit[5].Forexam ple,amemorybankconsisting ofmemorycellsmayberejectedbecauseofcouplingfaultsbe tweenadjacentmemorycells 5

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althoughthismayhavepassedthedesignspecication.Figu re1.5showsatypicalrow depictingtheincreasinginteractionbetweendesignandte st[6].refabricate Redesign and in case of faults components Defective TESTING FABRICATION DESIGN CONCEPTION PRODUCT ON_FIELD APPLICATION Figure1.5.Interactionbetweendesignandtestphasestoel iminatecouplingfaults 1.1Bus-basedinterconnects Withscalingdownoftechnology,theinterconnectassumesi ncreasingimportanceinthe design.Theinterconnectnotonlydominatesthedelayinthe circuitbutalsoconsumes about30%ofthetotaldynamicpowerinthedesign.Themostco mmoninterconnects are buses asbus-basedinterconnectsreducesthenumberofconnectio nscomparedtoother interconnectstyles.However,busesinvolvelonglengthso fwiresrunninginparallelandin closevicinityofoneanother.Withthedecreaseinthespaci ngbetweenthelinescompared tothethicknessofthewires,thecross-couplingcapacitan cebetweenthebuswiresbecome comparableandoftenexceedstheirwire-to-substratecapa citance. Adetaileddepictionofthevariouscapacitancesrelatedto theinterconnectswhichrun closetooneanotherisprovidedinFigure1.6.Theareacapac itance C area andthecapaci6

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Figure1.6.Thevariouscapacitancesinadesign tanceduetothefringeelds C fringe togetherconstitutethewire-to-substratecapacitance. Thecouplingcapacitance C xcoup existsbetweenclosewiresrunninginthesameplane.The couplingcapacitance C crossover existsbetweenclosewiresindierentplanes.When C xcoup + C crossover becomescomparableto C area + C fringe ,the crosstalk phenomenoncomesinto eect.Duetocrosstalk,thecircuitcouldproduceerroneou sresultsduetounwantedglitches onsomeofthelines.Alternatively,thecircuitcouldmalfu nctionduetoinduceddelayson someofthelineswhichcouldviolatetheirtimingrequireme nts.Thelineswhichcause glitchesanddelaysonotherlinesareknownas aggressors whilethelineswhichareaected bytheseaggressorsareknownas victims .Thecrosstalkeectsbetweenaggressorsand victimsaretwofoldandarestatedasfollows: 1.Ifthevictimwireisatasteadystatevalue(eitherlogica l`0'orlogical`1')whilethe aggressorwireisswitching(eitherfrom`0'to`1'orfrom`1 'to`0'),itcouldinducean unwantedpositiveornegativespikeonthevictimwire. 2.Ifthevictimwireismakingatransitionfrom`0'to`1'and theaggressorwireisalso makingatransitionfrom`0'to`1',thetransitionofthevic timwirewillbe hastened sincethetransitionisbeingaidedbytheaggressor.Ontheo therhand,ifthevictim 7

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wireismakingatransitionfrom`0'to`1'andtheaggressori smakingatransition from`1'to`0',thetransitionofthevictimwirewillbe delayed sincetheaggressoris nowopposingthevictim'stransition.Thetransitionofthe victimwirefrom`1'to `0',withrespecttotheaggressor'stransition,canbesimi larlyanalyzed. 1.2ASICdesignrow Beforegoingintothedetailsofcrosstalk,itisimportantt orefreshthetypicaltop-down designrowofApplication-SpecicIntegratedCircuits(AS ICs),inordertosubsequently appreciatehowthecrosstalkproblemcanbetackledatdier entabstractionlevelsofa design.Figure1.7showsthetop-downdesignrowofASICs.St artingwiththebehavioralleveldescriptionofadesign,typicallyintheformofacont roldata-rowgraph(CDFG), high-levelsynthesisisperformed.High-levelsynthesis( HLS)involvesthreestepsnamely, scheduling,allocation,andbinding.During scheduling ,individualoperationsintheCDFG areassignedtotimestepsinwhichtheyaretobeexecuted.Th isisfollowedby allocation whereresourcesareassignedtoimplementthedierentoper ations.Finally, binding maps individualoperationstodierentinstancesoftheresourc es.Attheendofhigh-levelsynthesis,wegetaregister-transferlevel(RTL)implementat ionofthebehavioraldescription wheretheentiredesignisdescribedintermsofasetofregis ters,functionalunits,andmultiplexersalongwithdatatransfersbetweenthem.Theinter connectionsbetweendierent componentsareaccomplishedthrough buses LogicsynthesisisthenperformedonthisRTLdesignduringw hicheachmoduleis describedintermsofitsgate-levelnetlist.Forexample,a 2x1multiplexerwillbedescribed intermsofaninverter,twoANDgates,andanORgate,asshown inFigure1.8. Theentiregate-levelnetlististhensubjectedtophysical -levelsynthesis.Physical-level synthesisconvertsthegate-leveldesigntothenallayout throughasequenceofsteps namely,partitioning,roorplanning,placement,routing, andcompaction[7]. Partitioning decomposesthegate-levelcircuitintosetsofsmallergate -levelcircuitssothatthesmaller circuitsmaybedesignedindependentlyandthencombined.S uchanapproachspeedsup 8

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RTL design High-level Synthesis Logic Synthesis Synthesis Layout Physical Layout Transistor-level design Gate-level design Behavioral model Figure1.7.Top-downdesignrow thedesignprocess. Floorplanning istheprocessofassigningapproximatedimensionsand shapestotheindividualgate-levelsubcircuitstodetermi netherelativepositionsbetween theseinthenallayout,usuallywiththeobjectiveofminim izingthelayoutarea.The outputoftheroorplanningphaseisthennalizedinthe placement phasewherethecircuit blocksareassignedtoactualcoordinates.Inthe routing phase,thepinconnectionsbetween theplacedblocksarecompletedusing buswires ,withtheobjectiveofminimizingboth delayandskewofcriticalsignals.Theseeectswillbedisc ussedingreaterdetailinthe subsequentchapters.Finally, compaction isperformedtoexplorewhetherthelayoutarea maybefurtherreducedbyeliminatinganyunusedspacebetwe enthemodules. 1.3High-levelestimation:anadvantage Eachdesignstagehasitsownmodelsforcrosstalk.Tradeos existbetweentheaccuracyandcomplexityofthesedierentmodels.Thehigherabs tractionlevelsofthedesign yieldmuchbetter design-spaceexploration thanthatofthelowerlevelsofabstraction.In otherwords,evaluationofdierentsolutionsandmovement fromonesolutiontoanother 9

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S I1I2 y y S I1I2 2x1 Mux y = S'.I1 + S.I2 Logic Synthesis Figure1.8.RT-leveltogatel-levelusinglogicsynthesis takesverylittletimeandcostatthehigherlevels.Forinst ance,analyticalexpressionsfor dynamicpowerestimationarepreferredoversimulationsin cethelatterisexpensiveand takesunreasonableamountsoftimeinmoderndesignscontai ningmillionsoftransistorsand wires.Thecostinvolvedindetectingerrorsandcorrecting themincreasesbyafactorof10 betweeneachabstractionlevelaswemovetop-downintheASI Cdesignrow[8].Thus,detectingcrosstalk-sensitivityatthegate-levelis10time smoreexpensivethandetectingitat theRT-level.Crosstalkminimizationinvolvingthephysic alsynthesisstepsofpartitioning, placement,androuting,islikelytobetentimesmoreexpens ivethanmakingarchitectural transformationstominimizeitbeforegeneratingthegatelevelnetlist.Thismotivatesusto thinkofnewtechniquestopredicteectsatthelowerlevels ofabstractionfromthehigher levelsofabstractionsoastominimizeexpensiveerrorsatt helowerlevels.Crosstalkisa problemwhichcouldcreatedesignclosureproblemsifdetec tedinthelaterstagesofthe design,oncemostofthelayouthasalreadybeenxed,sincet hereisverylittleroomto makechangesintheplacementandrouting.Thus,therearise sacriticalneedtodesigna fastandreasonablyaccurate crosstalknoiseestimator toaddressthecrosstalkproblemin theearlierdesignstages. 10

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However,thecrosstalknoiseproblemiscloselyrelatedtoa lotoflower-levelparameters whichcannotbeaccuratelydeterminedatthehigherabstrac tionlevels.Someoftheseare asfollows. 1.Thepositionsofthemodules,relativetooneanother.2.Therouteofeachwire.3.Theaggressorsofagivenwireinboththehorizontalandth everticalplanes. Forexample,(1)cannotbedeterminedbeforeroorplanningh asbeenperformed.Similarly,(2)and(3)cannotbedeterminedbeforeroutinghasbe enperformed.Thus,high-level crosstalkestimationbecomesahardproblemandmotivatesu stodevisetechniquestointegrateaccurateinformationfromthelowerabstractionleve lswiththeanalyticalestimation processatthehigherabstractionlevels. Inparticular,statisticalestimationmethodshavebeensh owntobeverypowerfulwhile estimatingdynamicpowerconsumptionindatapaths[9][10] .Themainadvantageofstatisticalestimationtechniqueslieintheirfastexecution timeswithoutlossofaccuracy. Ramprasadet.al.[11]andSatyanarayanaandParhi[12]furt herdemonstratetheusefulness ofusingword-levelstatisticalparametersduringhigh-le velpowerestimationmethods.The detailsoftheseapproacheswillbediscussedinthenextcha pter. 1.4Proposedapproachtothecrosstalkestimationproblem Thenotionofcrosstalkisgraduallychanging,aswillbeamp lydemonstratedinthe followingchapter,froma static phenomenonwhichdependsonasetofxedparametersto a dynamic phenomenonwhichdependsonthesignalvaluesoftheneighbo ringwiresatruntime.Inthiswork,wetreatthecrosstalkphenomenonasa pattern-dependent phenomenon. Inotherwords,whetherornotanaggressorwirewillcausecr osstalkonavictimwirewill dependontherelativesignalvaluesoftheaggressorandvic timwires.Anaggressorwill causeacrosstalkeventonavictimif 11

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1.Theaggressorisswitchingwhilethevictimisinasteadystate. 2.Theaggressoraswellasthevictimareswitching. 1.4.1Intra-buscrosstalkestimation Thersttypeofeventswillcausecrosstalk spikes or glitches onthevictim.Thesecond typewillcausecrosstalk delays onthevictim,dependingontherelativedirectionsinwhich theaggressorandvictimareswitching.Thus,thecrosstalk eectavictimexperiences essentiallydependsonthevaluesonthevictimanditsaggre ssorlines,oversuccessive intervalsoftime.Inotherwords,thecrosstalkeectdepen dsontheinputdatastreamon thebus.Givenaninputdatastream,wecancomputethetotaln umberofcrosstalkevents thatavictimlineexperiences.Ifthelengthofthedatastre amisknown,wecanassociate a crosstalkprobability witheachvictimlinewhichisadirectmeasureofit'ssuscep tibility tocrosstalk. Toestimatethecrosstalkprobability,weenumeratethecro sstalk-producingpatternson thevictim,usingthegeneralaggressor-victimcongurati onoftwoadjacentaggressorson eithersideofavictim,showninFigure1.9.Weproposeasimp le stream-basedestimator thatcomputesthecrosstalkprobabilityofavictimlineint hebus.Givenadatastream, thestream-basedtechniquesimplycountsthetotalnumbero fcrosstalk-producingpatterns anddividesitbythelengthofthedatastreamtocomputethec rosstalkprobabilityofa victim. However,dealingwithdatastreamsiscumbersomeandtime-c onsuming.Tospeedup theestimationtime,weproposea word-level statisticalcrosstalkestimator.Theinputto thisestimatorisasetofword-levelstatisticalparameter s(mean,standarddeviation,and lag-1temporalcorrelationcoecient)oftheinputdatastr eam,insteadofthestreamitself. Theoutputoftheestimatoristhebit-levelcrosstalkproba bilityofeachlineofthebus. Althoughthespeedupobtainedintheestimationtimeishigh ,thetimecomplexityis stillexponential,withrespecttothebuswidth.Inorderto alleviatethisproblem,weusea 12

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Cg Cg Cg Cx Cx Aggressor A1 Victim V Aggressor A2 Figure1.9.Aggressor-victimsimulationcircuit circularrightshift procedurethatmodiestheestimatortomaketheestimation timelinear withrespecttothebus-width. Weimplementedtheproposedapproachesandvalidatedthemf orseveraldierentdata environments,modeledasARMAsignals,aswellasbus-width srangingfrom8bitsto 32bits.Inotherwords,theproposedtechniquesarenotrest rictedtoaparticulardata streambutratheraredesignedtohandleanydatastreamfrom specieddataenvironments. Weestablishtheexactmatchinthecrosstalkprobabilities estimatedbytheproposed stream-basedestimatorandthatobtainedthroughHSPICEsi mulations.Atthesametime, wedemonstratethefasterspeedofthestream-basedestimat ioncomparedtoHSPICE. Subsequently,weusethestream-basedestimationasthebas isforcomparingtheaccuracy andspeedoftheproposedstatisticalestimationtechnique s. 1.4.2Inter-buscrosstalkestimation Weextendtheproposedword-levelstatisticalestimatorof intra-buscrosstalk,tomeasurecrosstalkbetweendierentwiresatthelayout-level. Whiledealingwithlayouts,it becomesimperativetoobtainaccurateinformationaboutth eplacementofmodulesinthe layoutandtheroutesofthewiresconnectingdierentmodul es.Hence,weintegratea roorplannerandglobalrouterinourestimationrowwhichen ablesustogettheplace-androuteinformation.Wethenform compositebuses insideroutingareas,usingwireswhich 13

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arelocatedinthevicinityofoneanother.WeperformRT-Lev elprolingonthedesign togettheword-levelstatisticsonthesecompositebuses.W ethenemployourstatistical estimatorstocomputethecrosstalkprobabilitiesoneacho fthesebuslines.Additionally, weanalyticallyestimatethemaximumnoisepulseamplitude onagivenvictimwireinthe layoutusingtheinformationfromtheglobalrouter.Thus,w eobtainthesusceptibilityof eachvictimbothintermsofthetotalnumberofcrosstalkeve ntsitissubjectedtobyits aggressorsaswellasthemaximumnoiseamplitudeitexperie nces. Startingwiththebehavioraldescriptionofadesigninterm sofadatarowgraph,weuse AUDI ,ahigh-levelsynthesissystemdevelopedbyourresearchgr oupatUSF,togenerate theRT-levelnetlistforeachdesign.UsingtheCadenceNCLa unchsimulator,wecreate ourownRT-levelprolertoobtainthedatavaluesonindivid ualwiresinthedesignatthe register-transferlevel.Usingapre-characterizedcelll ibrarygeneratedusingCadenceicfb, weusetheCadenceSiliconEnsemblesynthesistooltoperfor mroorplanningandglobal routing.Thetargettechnologyusedin0.35 CMOStechnology. 1.5Optimizationforcrosstalk Weusethecrosstalksusceptibilityinformationofeachvic timnettoexplorethebinding spaceandsearchforcrosstalk-awarebindingsolutionsdur inghigh-levelsynthesis.Weuse amodiedclique-partitioningalgorithmthattakescrosst alkactivityintoaccountwhile selectingedgestobindtoagivenregister.Comparisonswit htheregularbindingsolutions showcrosstalkactivityreductionsattheregisteroutputs 1.6Organization Therestofthedissertationisorganizedasfollows.Chapte r2willdiscusssomeof theexistingworksintheliteraturethathavetargetedtoso lvethecrosstalkestimationand optimizationproblemandhaveelucidatedtheadvantagesof usingstatisticalmodelsinhighlevelestimationproceduresforASICs.Chapter3willintro duceourapproachtotheintrabuscrosstalkestimationproblem.Inthischapter,weexpla inthe enumerative statistical 14

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estimatoralongwiththe stream-based estimatorwhichweuseasthebasisforcomparison. Chapter4willdemonstratethemodicationofthestatistic alenumerativetechniquetoget thestatistical non-enumerative techniqueandobtaintwoordersofspeedupintheruntime oftheestimationprocess.Chapter5willexplainhowweform ulatethe inter-bus crosstalk estimationproblemsoastointegratetheintra-buscrossta lkestimatoralongwithlayoutlevelinformationofthecircuitanddeterminewhichwires, atthephysical-level,aremost aectedbycrosstalk.Chapter6willproposeacrosstalkopt imizationprocedure,based onthecrosstalk-susceptibilityinformationprovidedbyt heestimators.Theexperimental setupsalongwiththeresultsandtheiranalysiswillbepres entedattheendofeachchapter. Finally,Chapter7willpresentconclusionsandthedirecti onsforfuturework. 15

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CHAPTER2 BACKGROUNDANDRELATEDWORK Thecrosstalkproblemhasassumedincreasingimportanceov erthelastfewyears.There hasbeenresearchtargetingestimationandoptimizationof crosstalk,atvariouslevelsof designabstraction.Inthischapter,wediscussthisresear ch.Inparticular,wediscussthe variousmodelswhichhavebeenusedtocapturethecrosstalk eectincircuitsaswellasthe keyideasusedincrosstalkoptimization.Specialemphasis isgiventostatisticalmodeling ofpowerconsumptionanditsadvantagesascomparedtoother modelssince statistical modeling iscentraltoourtechniques.Wealsodemonstratethenovelt yofourapproaches andhowtheytintotheoverallASICsynthesisrow.2.1Layout-levelcrosstalkestimation In[13],anecienttechniqueforestimatingthemaximumcou plednoiseforon-chip interconnectsispresented.Thistechniqueisadirectappl icationofcontroltheory.The transferfunctionfunctionforthecircuitwiththeaggress orandvictimnetsiscomputed. Aninputvoltageintheformofaniterampisappliedtotheag gressornet.Thenal valuetheoremisappliedtothevictimnetinordertogetanup perboundonthecoupled noiseonthevictim.Thistechniquesuersfromthetwofollo winglimitations: 1.Sincethenoiseonthevictimnetisdependentontheslopeo ftheaggressorvoltage, thenoiseonthevictimcanincreaseinanunboundedfashioni ftheslewrateofthe aggressorvoltageisveryfast. 2.Thistechniquedoesnotaccountforthedependenceofthec ouplingnoiseonthe wire-to-substratecapacitancesoftheaggressornetandth evictimnet. 16

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Hence,Kuhlmannet.al.[14]improveontheDevganmetrictoa ccuratelyestimatethe couplingnoise,basedonthesinkcapacitancesofthevictim andtheaggressor,thecoupling capacitancebetweenthem,andtherisetimeoftheaggressor net.Byecientlysolvingthe smallsignalmodelequationsforthevictimandaggressorne ts,theestimationcomplexity isimproved. Varioustimingandglitchdetectionissuesareanalyzedusi ngthe charge-sharingmodel [15]. Inthismodel,thenalvoltageatanynodeinthecircuitisex pressedasaratioofthetotal chargetothetotalcapacitance.Duringatransitionatanod e,thenodalvoltageisexpressedasafunctionofthecapacitors'currentsrowingtot hegroundnode.Thismodel servesasareferenceforcrosstalkestimationheuristicsb ecauseofitsabilitytomodelnodal voltages.Vittalet.al.leverageonthisintheirattemptto addressthecrosstalkproblemat thelayoutlevel[16][17][18].Theymakeseveralnovelmodi cationstothecharge-sharing modelandderiveanalyticalexpressionsforthecoupledint egralaswellasanupperbound ontheamplitudeofthenoisevoltage.Someofthekeydieren ceswiththe chargesharing model areasfollows: Usingdynamicnoisemarginsasopposedtostaticnoisemargi nsusedintheprevious models .Dynamicnoisemarginsaremoreaccurateastheyaccountfor thepulse amplitudeaswellasthepulsewidthofthenoise[19][20][21 ][22].Thus,anoisepulse ofsignicantamplitudebutverysmalldurationiscorrectl ydeterminedtobeharmless usingdynamicnoiseanalysissincethevictimnetswillnotb edriventoanyerroneous valueinsuchashorttime. Accountingforthedependenceofthecrosstalknoiseonthed rivestrengths .The previouslyusedchargesharingmodelfailstoaccountforth isdependence.Suppose thereisavictimwire v andtwopotentialaggressorwires, w 1 ,withasmallshared chargeaswellassmalldriveresistance,and w 2 ,withalargersharedchargeanddrive resistance.Further,letthefrequencyoftransitionson w 1 begreaterthanthaton w 2 Then,accordingtothechargesharingmodel,itisbettertor oute v alongside w 1 but accordingtoVittal'smodel,itisbettertoroute v alongside w 2 .Thisisbecausein 17

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M C x C 1 R 1 R 2 C 2 V m V o O Figure2.1.Equivalentcircuitforcomputingcrosstalknoi seamplitude Vittal'smodel,althoughthesharedchargebetweenthevict imandaggressorismore, thetotalcouplednoiseonthevictimislesserduetosmaller switchingfrequencyof theaggressor. Accountingforthedependenceofcrosstalknoiseontheslew rateoftheaggressor Vittal'smodelincreasesoverlapsofthevictimwithnetswh ichswitchslowlyinorder toreducetheoverallcrosstalkonthevictim.Thetolerable overlaplengthsarehigher thanthecharge-sharingmodelresultinginmorerexibility duringrouting. BasedontheFigure2.1,theanalyticallycomputedboundont hecrosstalknoisepulse isprovidedinEquation2.1. V p = 1 1+ C 2 C X + R 1 R 2 (1+ C 1 C X ) (2.1) where R 1 and R 2 arethelumpedresistancesoftheaggressorandvictimnetsr espectivelywhile C 1 and C 2 arethewire-to-groundcapacitancesoftheaggressorandvi ctimnets respectively. C X isthecouplingcapacitancebetweentheaggressorandvicti m.Themaximumboundonthenoisepulseamplitudeisusedtodetermineth enoise-criticalnets.The criticalityofeachnetwithrespecttocrosstalkistheninc orporatedintothecostfunction ofagreedychannelrouter.Theroutingsolutionsarefoundt obeoptimizedforcrosstalk comparedtothestandardgreedychannelroutingsolutionsw hichdonotconsidercrosstalk. 18

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Vittalet.al.furtherprovideananalyticalexpressionfor thecrosstalkpulsewidthin[18], asshowninEquation2.2. V width = K b 1 (2.2) where K = P R i 2 P ( o ) C X i R i and b 1 = P C i 2 C ) C i R ii ,where C X i isthesumofthe couplingcapacitancesasseenfromnode i P ( o )istheunionofthevictimdriveresistance andthesetofresistancesinthepathfromroot i tonode o C isthesetofallcapacitors,and R ii istheresistanceseenacrosscapacitor C i withallothercapacitancesopen.Theaccuracy oftheproposedestimationequationsfortheamplitudeandt hepulsewidth,withrespect toHSPICEsimulations,isfoundtobehighwithaverageerror slessthan10%andthese parametersareincludedinthecostfunctionofoptimizatio ntechniquesnamely,transistor sizing,wireordering,andwirewidthoptimization. Typically,thecrosstalk-induceddelayincircuitsisesti matedbysuperposingtheswitchingwaveformofthevictimandthenoisewaveformofthevicti mwhenitis quiet .However, thisisfoundtounderestimatetheactualdelaymeasure.Tom aketheestimationprocess moreaccurate,atechniqueispresentedbyTsaiandSadowska [23]thatintroducesthe conceptof dynamiccouplingnoise .Thisaccountsforthedependenceofthecrosstalknoise amplitudeandpulsewidthontheskewoftheaggressorwavefo rm. 2.2Gate-levelcrosstalkestimation AnoveltechniquetominimizecrosstalkinProgrammableLog icArrays(PLAs)ispresentedbyTienet.al.in[1].PLAsareparticularlysuscepti bletocrosstalkasco-planar productlinesruninclosevicinityofoneanotherforlongdi stances.Bysimulationofthe genericaggressor-victimcongurationshowninFigure1.9 ,theauthorsobtainthepeak voltageofthevictims.Thetargettechnologyusedbytheaut horsisTSMC0.35 m .The couplingcapacitanceandpeakvoltagesaresummarizedinTa bles2.1and2.2respectively. 19

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Table2.1.Couplingcapacitanceoftwowiresfordierentov erlappinglengths(reproduced fromTienet.al.[1]) MetalLayer 100 m 300 m 500 m 1000 m M2 C x 9.4fF 25.6fF 41.8fF 82.3fF M2 C g 4.9fF 13.7fF 22.4fF 44.4fF M4 C x 14.6fF 40.2fF 65.8fF 129.8fF M4 C g 3.3fF 9.0fF 14.6fF 28.8fF Table2.2.Crosstalknoiseofthevictimproductlinefordi erentproductlines(reproduced fromTienet.al.[21]) MetalLayer #ofaggressors 100 m 300 m 500 m 1000 m M2 1 131.7mV 231.9mV 294.5mV 354.9mV M2 2 260.4mV 453.2mV 568.0mV 690.6mV M4 1 190.5mV 331.4mV 411.7mV 486.3mV M4 2 375.1mV 655.0mV 813.2mV 990.0mV Sinceseveraloutputsmayshareaproductterm,thetechniqu econsiderstheoutputset ofeveryproductlinei.e.,thesetofoutputswhichsharetha tproductline.Avictimlineis considered crosstalkimmune ifitsoutputsetisasubsetoftheoutputsetsofitsaggresso rs. Thisisbecauseifeachproducttermgeneratedbyavictimcan begenerateddierent aggressors,wecanremovethevictimlinealtogether.Theau thorsndgoodorderingsof boththeproductlinesaswellastheinput-outputlinesinor dertomaximizethenumberof crosstalk-immune lines.Thereorderingalsoservestoreducethewirelengths inthePLA.An exampleofthereductioninwirelengthduetoinput-outputr eorderingisshowninFigures 2.2and2.3. BuyukashinandNajm[24]predicttheinterconnecteectsdu ringhigh-levelpowerestimationbyestimatingtheaverageinterconnectlength.Gi venahigh-leveldescriptionof thecircuit,theauthorsusethewell-knownRent'srulealon gwithanestimationofthegate countinordertocomputetheinterconnectlength. Intermsofthedesignstyle, domino logicisverypopularamongstcontemporarydesigners.Theperformanceofthisdesignstyleishowever,intric atelyconnectedtothequality oftheinterconnectdesign.In[2],theauthorsaccountforc ross-couplingamongstinter20

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I2I3I4 I1 P1P2P3P4P5P6P7 O1O2O4O5 O3 Figure2.2.AnexampleofaPLA(originalconguration) I2 O2 I3I4I1O5O4O3O1 P4 P3P6P1P2P7P5 Figure2.3.Reductioninwirelengthusingreordering 21

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connectwireswhileformulatingthecycle-averagedpowerm odeloftheinterconnect.The cross-couplingisaddedasaconstraintwhilecomputingthe maximumwiredelay.Thecouplingpoweristhenminimizedusingasimulatedannealingap proachbymoving,swapping, andpermutingthewiresintheinitialroutingsolution.2.3High-levelestimationofcircuitparameters Researchinliteratureexiststhatattemptstoestimatecir cuitparameterssuchaspower consumption,area,circuitdelay,switchingactivityande ven,couplingeectsatthehighlevel.Wesummarizethisworkasaprecursortotheestimatio nofcrosstalkeectsatthe high-level. Inparticular,powerestimationaswellasoptimizationdur inghigh-levelsynthesis,have beenextensivelyresearched[25][26][27][28][29][30][3 1].Sincethedynamicpowerisquadraticallydependentonthesupplyvoltage[32],acommontechni queistousemultiplesupply voltagesfordierentpartsofthecircuit.Componentsonth ecriticalpathsareactivated usingthehighervoltagessoastostrictlyobeythetimingco nstraints.Thenon-criticalcomponentsareactivatedusingalowersupplyvoltagesoastomi nimizetheoveralldynamic power[33][34].A prole-driven approachtosynthesizedesignswithminimumswitching activityispresentedin[35][36][37].Variousarchitectu raltransformationsareusedtooptimizeregistersandinterconnectsduringthesynthesispr ocess[38].Thedesign,specied asadatarowgraph,isinitiallystimulatedusinguser-supp liedinputpatterns.Probesare insertedatvariousregionsofthecircuitspecicationtom onitoreventactivity.Alibraryof moduleswhoseparametersaredeterminedthroughcharacter ization,isusedinthelayout generationphase.ThelayoutsaregeneratedusingtheLager IVSiliconCompiler[39].For validationofthepowerestimationprocedure,switch-leve lmodelsofthelayoutareextracted andvalidatedusingtheIRSIM-CAPsimulator. Anothertechniqueistodynamicallyaltertheclockfrequen cytoacomponentdepending onwhetheritispartofthecriticalpathornot.Onceagainco mponentsonthecriticalpath arefedwithahigherclockfrequencywhilenon-criticalcom ponentsarefedwithalowerclock 22

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frequencytominimizedynamicpowerIn[40],thelowerfrequ encyoperationsarescheduled inearliertimestepswhilehigherfrequencyoperationsare scheduledinlatertimesteps. Subsequently,someofthehigherfrequencyoperationsarer egroupedwithlowfrequency operationstoobeythetimeconstraints.Mostoftheseappro achesaretime-constrained i.e.,thethroughputofthedesignisgiven.However,themul tiplevoltageapproachhas successfullybeenappliedtotheresource-constrainedpro blemtoo[41][42].IntegerLinear Programming(ILP)modelsforenergyandtransientpowermin imizationduringthesynthesisprocesshavebeenproposedin[43].Thecyclepowerfu nction(CPF)expressedin termsoftheaveragepowerconsumptionandpeakpowerdiere ntialaccuratelycaptures thepowercharacteristicsofdatarowgraphsinsuchmultipl evoltagecongurations.Further,theauthorsproposeatechniquetomodifytheusuallyn on-linearnatureofthecycle powerfunctionsoastouseILPsolutionsonit[44].Anothera pproachtoreducethedynamicpowerconsumptionbyreducingtheswitchedcapacitan ceinsidedierentmodulesis presentedin[45]. In[46],transitiondensity[47]isusedasahigh-levelmetr icfortheswitchingactivityin digitalcircuits.Thetransitiondensityisdenedastheav eragerateofswitchingatacircuit node.Theaveragepowerconsumptionisapproximatelyhalft hetotalpowerconsumption. Thus,fromEquation1.1, P cap;avg = 1 2 C L E ( sw ) V 2 DD f = 1 2 C L V 2 DD E ( sw ) T (2.3) where E ( sw )isthetotalnumberoftransitionsoveraninterval T .Thelimitlim T !1 E ( sw ) T isreferredtoasthetransitiondensity.Usingastochastic modelofthebinarysignalsatthe nodes,thetechniquepropagatesthetransitiondensitythr oughthecircuitmodules.Thisis particularlyusefulforlargecircuitswhichwouldotherwi seneedextensivesimulationwith largevectorstreamstocomputetheswitchingactivityatth evariousnodes. Conceptsfromresearchareasasdiverseaseconomicsandmec hanicshavebeenincorporatedintoelectronicdesignautomationtargetingpowerop timizationandareaoptimization. In[48][49],theauthorsusetheauction-basednon-coopera tivegametheorybasedonNash 23

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equilibrium[50]tooptimizepowerduringbehavioralsynth esis.Ontheotherhand,in[51], theauthorsusetheconceptofthemechanicalspringforceto minimizetheareaofacircuit foragivenlatency. Thehigh-levelestimateofthegate-countisusedbyNemania ndNajm[52]asahighlevelmeasureofthecircuitarea.Thegate-countisestimat edbyconvertingmultiple-output Booleanfunctionsimplementedbythecircuitintoanequiva lentsingle-outputfunctionand thenusingthe on-sets i.e.,themintermsforwhichthefunctionistrueand o-sets i.e., themintermsforwhichthefunctionisfalseofthenewfuncti on,todeterminethepossible sharingofgatesintheoriginalmulti-outputfunction.Byc onsideringsharing,theminimum numberofgatesandthus,theminimumareaisestimated.Howe ver,thetechniqueis currentlyrestrictedtocombinationalcircuitsanddoesno tworktoowellforcircuitswhich containlargearraysofXORgates. In[53],theauthorsestimatethepowerconsumptionattheRT -levelofadesignby using entropy asameasureoftheaverageswitchingactivityinthecircuit .Theentropy isdenedastheinformation-carryingcapacityofarandomv ariable.Theentropyplot ofaBooleanvariableisaperfectbell-shapedcurve,asshow ninFigure2.4.ABoolean variablewithprobability p =0.5hasavalueof`1'50%ofthetime.Thus,itcanmake themaximumnumberoftransitionsandcancarrythemostinfo rmation.Thetechnique associatesanentropywitheachBooleanvariableinaBoolea nfunctiontobeimplemented bythecircuit.Thus,eachfunctionhasasetofinputandoutp utentropies.Fromthese, theaverageentropyateverynodeinthecircuitcanbedeterm ineddependingonwhether itservesasaninputnodeoranoutputnodeorboth.Theaverag epowerconsumptionis thenapproximatedasaproductoftheactivityandthearea.A tthehigh-level,theareais estimatedtobeproportionaltothenumberofdon't-careter msintheBooleanfunction. Further,theauthorsuse petri-nets inordertomodeltherealdelayofbothlogicgates andinterconnectsin[54][55].Therealdelayvaluesareuti lizedincomputingtheoverall switchingactivityinthecircuit.Anygivenlogiccircuiti sinitiallymodeledasagatesignalgraphwhichisthentransformedintoahierarchicall ycoloredhardwarepetri-netand 24

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0.01.0 0.5EntropyProbabilityFigure2.4.Bell-shapedcurveofentropyforbooleanvariab les simulatedtoestimatetheswitchingactivity.Yetanothera pproachtoestimateswitching activityispresentedin[56]whichusestheBayesiannetwor kmodelfromstatistics.Inthis, Bayesiannetworksareusedtocapturecomplexconditionald ependenciesbetweendierent nodesinacircuit.Thetemporalandspatialcorrelationsof theswitchingactivityatanode isexpressedasaswitchingprobabilitymodel.Theseswitch ingprobabilitiesarepropagated veryecientlythroughtheBayesiannetwork. Thedependenceofcrosstalk-induceddelaysinbuses,onthe inputdatatothebus,has beenanalyzedin[57].Eachpatternhasanassociateddelay. Usingacharacterizationtechnique,variousdelay-groupsareformedsuchthateverydata patterntobetransmittedover thebusbelongstooneofthosegroups.Thetechniqueusesafa sterclockanddynamically controlsthenumberofcyclesrequiredtotransmitanygiven datapattern,basedonits delayvalue.Althoughthistechniqueimprovestheperforma ncebyover30%,itdoesnot accountforthecrosstalk-inducedspikesonthedatabus.no thampered. 2.3.1Worst-casecrosstalkmetrics The worst-case crosstalknoiseanddelaymetricsareoftenusedintheanaly sisofcircuit performance[58][59].Theproponentsofthisapproachargu ethatifthecircuitisdesigned fortheworst-caseperformance,nofataleventswilloccurd uringitsoperation.Theworstcasenoiseanddelayaretypicallyevaluatedusingoneofthe followingtwomethods. 25

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1.Thenoiseresultingfromseveralaggressorsswitchingat thesametimeisdetermined usingthe superposition theoremi.e.,consideringonlyoneaggressortobeactivean d theotherstobesilentatatime,andevaluatingthepeaknois eonthevictimfromthe activeaggressor.Thetotalnoiseisthenasummationofthep eaknoisesfromeach aggressor[13][60][61]. 2.Thetotalcouplingnoiseonthevictimiscomputedbyassum ingthattheinputsto alltheaggressorsofthevictimhavethesamearrivaltimes. Inotherwords,the aggressorsswitchsimultaneously[62][63]. However,theworst-casemetricsarepessimisticinnature. Inreality,theworst-case rarelyoccursandalthoughthedesignsaremademorerobust, performanceisoftensacriced.Forexample,iftheclockfrequencyofabusissetaccor dingtotheworst-casedelay onthebus,itmaybequitelow,thusmakingthesystemslower[ 57].Inreality,theworst casedelaymayoccurveryrarely.Thus,dependingontheappl ication,itmaybebetterto setthefrequencyaccordingtotheaveragedelay.Thiswillr esultinafastersystemwhich maystillbesusceptibletotheworst-casecrosstalk.Sucha napproachistakenin[64]where the instabilityperiods oftheaggressorsofagivenvictimarecomputedfrom: Theinstabilityperiodsoftheprimaryoutputsgivenbythed esigners. Thegatepropagationdelayscomputedusingtiminganalysis Fromthese,itispossibletocomputethetimeintheclockper iodatwhichasignal makesitstransition.Thistransitionintervalofasignali scalleditsinstabilityperiod. Fromtheinstabilityperiodofsignals,thenumberof active aggressorsforagivenvictim canbecomputed.This,alsoknownasthe maximalnoiseconguration ,resultsinamore realisticestimateoftheworst-casenoiseonthevictim. 26

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2.4Crosstalkoptimization Sofar,wehavelookedatcross-couplingestimationtechniq ues.Theestimatesobtained areusedinseveraloptimizationprocedurestominimizethe crosstalkincircuits.Welook atsomeoftheseoptimizationtechniques.2.4.1Shielding Oneofthesimplesttechniquestominimizecrosstalkistous e shieldwires inbetween lineswhicharehighlysusceptibletocrosstalk.Theseshie ldwiresarekeptatzeropotential, inordertoactasaneectivebarrierbetweenthevictimandt heaggressor,asshownin Figure2.5.IntheFigure,thereisashieldingwireatzeropo tentialbetweenlines l 2and l 3.Thus,theselineswillnotaectoneanotherwithrespectt ocrosstalk.However,line l 2maystillsuerfromcrosstalkduetoline l 1sincethereisnoshieldingbetweenthem. However,thedisadvantageofthistechniqueisthatitincre asestheareaoverheaddueto thelargenumberofshieldwireswhichwillberequiredbetwe envictimsandaggressorsin largedesigns. Tocountertheareaoverheadproblem,SaxenaandGupta[65]i ntegratetheseparate stepsof powerrouting and signalrouting tominimizethenumberofshields,whilesatisfying allshieldingconstraints.2.4.2Wirereordering Anotherpopularcrosstalkminimizationtechniqueiswirer eordering.Reorderingisthe shuing ofwires,therebychangingtheiradjacencieswithrespectt ootherwiresandmaking themimmunetocrosstalkeects[66].Figure2.6illustrate stheoriginalandreordered congurationsofabus.Intheoriginalconguration,itmay beseenthatlines l 1, l 2,and l 3areallsusceptibletocrosstalk.Thetransitionon l 2isdelayedduetotheopposing transitionon l 1whilethetransitionon l 2inducesadownwardspikeon l 3.However,by reorderinglines l 2and l 3,thedelayeecton l 3iscancelledduetotheopposingtransitions 27

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l1l2 l3 g, l3 g, l2C Cg, l1C(Shielding wire) GND Figure2.5.Shieldingwireinputvictimandaggressorl2 l3 l1 l2l3 l1 Reordered Original Figure2.6.Eliminatingcrosstalkbybusreordering onitsaggressors l 1and l 2.Atthesametime, l 2becomesfartherremovedfrom l 1,making itimmunetoeectsfrom l 1. 2.4.3Busencoding Crosstalkhasbeenrecognizedasadatapattern-dependentp henomenonasopposedto itspreviousnotionofbeingastaticphenomenon.Whilebusr eorderingentailskeepingthe datavaluesonthebuslinesconstantwhilechangingtheorde rofthebuslines,thebus encodingtechniquekeepsthephysicalorderingofthebusli nesconstantwhilechangingthe datavaluesonthebuslinesaccordingtoan encoding scheme.Thistechniquehasbeen 28

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b n b RECEIVER DECODER channel ENCODER SENDER Figure2.7.Communicationchainmodel0 0 0 1l1l2l2 l1 Encoding0 1 0 0 0 1 1 0 Figure2.8.Eliminatingdelaywithself-shieldingcodes previouslyusedforminimizingtheglitchpoweractivityon adatabus[67].Inthecase ofcrosstalk,thedatavaluesareencodedsoastominimizecr osstalkactivitybeforebeing transmittedalongthebus.Atthereceivingend,theyaredec odedbacktotheiroriginal values.Figure2.7illustratesthecommunicationchain. Abusencodingschemetopreventcrosstalkdelayispresente din[68].Here,adjacent linesarepreventedfromswitchinginoppositedirectionsb yusing self-shielding codes,as showninFigure2.8.Inthegure,lines l 1and l 2originallyswitchinoppositedirections, causingcrosstalkdelayoneitherwire.However,byencodin geachbitusingits2-bitbinary value,adjacentlinesarepreventedfromswitchinginoppos itedirections. Anothercrosstalkminimizationtechniqueusingcapacitan ceoptimizationisproposed in[69].Thisusesaplacementtechniquethatplacesthebuslinesnon-uniformly,depending ontheactivityinformationofthelines.Thetechniquemini mizescrosstalkpowerwithout anyincreaseinthecomplexityofthedesign.Severaldiere ntalgebraic,permutation-based, andprobabilisticbus-encodingschemestargetingcrossta lkminimizationarediscussedin [70][71][72][73]. 29

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2.5Word-levelstatisticalestimators Theinherentadvantageofquickdesign-spaceexplorationa tthebehavioral-levelofdesignsmotivatesdesignerstodevelopestimatorswhichcana ccuratelypredictthearea,delay,andpowerparametersfromhigh-levelsofdesignabstra ction.Inparticular,statistical, word-levelestimatorshavebeendevelopedfordynamicpowe restimation[9]andtransition activityestimation[11][12].Sinceword-levelstatistic siscentraltothemethodsthatwe proposeforcrosstalkestimation,welookatsomeoftheexis tingrelatedestimatorsforpower consumptioncloselyinthissection. LandmanandRabaey[9]proposedaword-levelstatisticalme thodusinga dual-bittype (DBT)techniquetoestimatethedynamicpowerconsumptioni ncircuitdatapathsatthe architecturallevel.Thedynamicpowerconsumptionisaec tedbytheswitchingactivityin thecircuitinputsandedges,asshowninEquation1.1.Thedu al-bittechniqueessentially capturesthedependenceofswitchingactivityonthesignal statisticsusingaccurate\blackbox"modelsforthedigitalcircuitsusingamodulecharacte rizationprocess.Itaccountsfor boththeuncorrelatedlower-orderbitsaswellastheheavil ycorrelatedhigher-orderbitsin aword. Thedynamicpowerconsumption P D atanynodeinacircuitisdirectlyproportionalto theproductoftheloadcapacitance C L andtheswitchingactivity E ( sw )atthenode,as showninEquation1.1.Thus, P D / C L E ( sw )(2.4) TheDBT-techniquemodelsthemodulecapacitanceandtheswi tchingactivityinside everymoduleseparately.TheDBT-modelcharacterizesthe modulecapacitance insideevery modulebyusingvarioustypesofinputstothemodule.Thus,i tgeneratesablack-boxmodel ofthecapacitanceinsideeachmodule.Withtheassumptiont hatthetotalcapacitance insideamoduleisafunctionofits\size",theDBT-techniqu eusestheseparameterizable capacitancemodelstoestimatethetotalcapacitanceinsid ealargemodule. 30

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BP0BP1 MSBLSB -0.99-0.8-0.5-0.2 0.00.20.40.70.99 0 15 0.00 0.500.25 0.350.10 rP(0 -> 1)UWN signFigure2.9.Dierentregionsinadatawordbasedontransiti onactivity ThemaindierencebetweentheDBT-modelandpreviousmodel sisthatitaccountsfor correlatedtransitionsaswellasrandomtransitionsamong databits.Forrandomword-level datavalues,theprobabilitythatabitiseither`0'or`1'is 0.5.Thus,theprobabilityofa bit-transitionfrom`0'to`1'iscomputedasfollows: P (0 1)= P (0) P (1)=0 : 5 2 =0 : 25(2.5) However,inastreamofword-levelvalues,onlysomeofthebi tsinawordarefoundto obeythisrelationship.Bitswhichobeytheaboverelationc onstitutethe UniformWhite Noise (UWN)regioninthedataword.Ontheotherhand,thehigheror derbitsaremore correlated.Infact,thehighestbitsaretypicallysign-bi tsinthedatawordandformost real-timesignals,thesebitshavecorrelationcloseto1.0 .Suchbitsconstitutethe sign region ofthedataword.Thus,basedontheseobservationsfromthec haracterizationprocess,a datawordcanbesplitintothreedistinctregions,separate dbytwo breakpoints BP 0and BP 1,asshowninFigure2.9.Thepositionsofthesebreakpoints aredependentonthe numberofbitsrequiredtorepresentthenumbersinthedatas treamwithalltheunused bitsbeingpartofthesignregion. 31

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UU UU + + + + CCCC+ + + -+UUC UU UUFigure2.10.Capacitivecoecientsfordierentsign-bitt ransitions Thebreakpoints BP 0and BP 1canbeexpressedasfunctionsoftheword-levelstatistica l parametersmean ,standarddeviation ,andlag-1temporalcorrelationcoecient BP 0= log 2 + BP 0 BP 1= log 2 ( j j +3 )(2.6) (2.7) Tocomputethecapacitanceswitchedbythedierentregions oftheword,eachmodule hasdierentcapacitivecoecientsfortheUWNandsignregi onsofthedataword.The whitenoiseregionhasasinglecapacitivecoecient C UU .Ontheotherhand,thecapacitive coecientforthesignedregionisafunctionofthesetofcap acitivecoecientscorresponding tofourdistincttransitionsofthesignbits,asshowninFig ure2.10.Thisleadstoaseriesof capacitivecoecientswhicharestoredaslook-up-tables. Thus,thepoweranalysisprocess isreducedtoaseriesoftable-lookups. Ramprasadet.al.[11]presentanotherword-leveltechniqu etoestimatethebit-level transitionactivityinsignals.Theymakeasimilardistinc tionbetweendierentregions ofadataword,basedonthelag-1temporalcorrelationofthe bits.Inthismethod,the intermediateregionbetweenthewhitenoiseandthesignedr egionistreatedasaseparate regionwherethecorrelationisassumedtolinearlyincreas efromthewhitenoisevalueto thesignedvalue,asshowninEquation2.8. 32

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Statistics Propagation 1 12 2 2 1 m s r m s r 3 m s r 3 3 + Figure2.11.Statisticspropagationinanadder i =0 ; ( i
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Theadvantageofusingword-levelstatisticsofsignalsaso pposedtotheactualsignal valuesisthatthesestatisticscanbepropagatedfromprima ryinputstoprimaryoutputs veryquickly.ForexampleintheaddercircuitinFigure2.11 ,giventhestatistics 1 1 1 and 2 2 2 atthetwoinputs,wecandirectlycomputethestatistics 3 3 3 atthe outputoftheadderasfollows: 3 = E [ x 3 ( n )]= E [ x 1 ( n )+ x 2 ( n )]= 1 + 2 2 3 = E [ x 23 ( n )] 23 = 2 1 + 2 2 +2 E [ x 1 ( n ) x 2 ( n )] 2 1 2 3 = E [ x 3 ( n ) x 3 ( n 1) 23 2 3 = 1 2 1 + 2 2 2 + E [ x 2 ( n ) x 1 ( n 1)+ E [ x 1 ( n ) x 2 ( n 1) 2 1 2 2 3 (2.10) Thecross-covariancesbetweenindependentsignalssimply reducestotheproductof theirmeans.Forcorrelatedsignals,thecross-covariance sbetweengroupsofprimaryinputs maybepre-computedandstoredbeforebeginningpropagatio nofthestatistics.Thus,the statisticsattheoutputofeveryresourceinthecircuitmay becomputedanalytically. 2.6Dataenvironments TheusefulnessofanyproposedtechniqueincontemporaryVL SIresearchisdemonstratedbyapplyingthemto dataenvironments .Ifatechniqueworkswellforagivendata environmente.g.,video,itessentiallydemonstratesthea pplicationofthetechniquetothat domain.Thisisavastimprovementovertechniqueswhichare limitedtospecicdata streamsandcannotbeappliedtoanygivenapplicationdomai n. 34

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Theeectivenessofusing AutoRegressiveMovingAverage (ARMA)modelsingeneratingdataenvironmentswasdemonstratedin[11].ARMAmode lsarecommonlyusedto representreal-timesignaldomainssuchasspeechandvideo An( N;M )-orderautoregressivemovingaveragemodel( ARMA ( N;M ))canberepresentedas x ( n )= d i r ( n i )+ a i x ( n i )(2.11) wherethesignal r ( n )isawhitenoisesourcewhosemeanvalueiszero,and x ( n )isthe signalbeinggenerated[11][12].Thevariable i givestheorderoftheARMAmodel.For instance, i =1givestherstorderARMAmodel.Inthismodel,thesignal x ( n )isrelated toitsvalueinthepreviousinstant.Thecoecients d i and a i maychosensoastominimize themean-squarederror.Ifthesecondtermiszero,thesigna l x ( n )ispurelydependent onthewhitenoiseinputandisindependentofthepreviousva lue x ( n 1).Ifthesecond termisnon-zero,then x ( n )isdependentonthepreviousvalue.Inthiscase,thetempor al dependenceisgivenbythetemporalcorrelationcoecient x .Thescalingfactorofthe whitenoisegivesthemean x whileanyadditionaltermgivesthestandarddeviation x of thesignal x ( n ).Thus,themodiedARMAmodelis x ( n )= x r ( n )+ x + x x ( n 1)(2.12) Thus,foragivensetofword-levelstatistics x x x ,wecangenerateadatastream correspondingtothesestatistics.Thisisusefulwhilecom paringourword-levelstatistical techniquesagainstdetailedHSPICEsimulationsandthestr eam-basedestimationprocedures.2.7Summary Tosummarize,thischapter 1.proposedcrosstalkestimatorsandmetricsatvariouslev elsofdesignabstractions. 35

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2.reviewedpopularcrosstalkoptimizationtechniques.3.summarizedword-levelstatisticalestimatorswhichhav ebeenpreviouslyusedtomeasurethetransitionactivityatcircuitnodes. 4.discussedtheusefulnessofdataenvironmentmodelingan dthetechniquestomodel them. Fromtheliteraturesearch,ourobservationwasthattherei sadearthoftechniques whichattempttotacklethecrosstalkproblematthehigh-le vel.Moreover,thereisnowork thatattemptstomodelthecrosstalkproblemstatistically .Thisistheprimarymotivation forthecrosstalkestimationandoptimizationtechniquest hatareproposedinthiswork. Thesubsequentchapterspresentthesetechniquesindetail 36

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CHAPTER3 INTRA-BUSCROSSTALKESTIMATIONUSINGWORD-LEVEL STATISTICS Thischapterintroducesourapproachtothecrosstalkestim ationproblem.Itformally statestheproblemthatwetrytoaddressanddetailsthekeyc ontributionsofthesolutions thatwepropose.Twohigh-leveltechniquestoestimatethep robabilityofcrosstalkevents onsignallinesofasystembusarepresented:(1)Givenaninp utdatastream,therst techniquesimplyestimatesthenumberofcrosstalkeventso neachlineofthebus.Themain drawbackofthistechniqueisthattheexecutiontimeisprop ortionaltothestreamlength. Thisisovercomebythesecondtechnique.(2)Giventhewordlevelstatisticalparameters, namelymean,standarddeviation,andlag-onetemporalcorr elationcoecient,weestimate thebit-levelcrosstalkprobability.Experimentalresult sfordatastreamsfromdierent dataenvironments,comparedagainstdetailedHSPICEsimul ations,arepresented.The stream-basedtechniquematchestheHSPICEsimulationsexa ctlywhileaverageerrorsof lessthan7%areobtainedforthestatisticalenumerativete chnique.Thecrosstalkestimation timeusingthestatisticalmethodissignicantlylessthan thestream-basedtechniqueand HSPICEsimulations.3.1Modelingthecrosstalkestimationproblem Asdiscussedinthepreviouschapter,thereisanacuteneedo fhigh-levelestimation techniquesofcrosstalk.Theabilitytopredictdetailsabo utthelower-levelsofdesign abstractionlikethephysical-level,fromthehigherlevel s,providestremendousleverage tothedesignerinexploringthedesign-spaceecientlyand generatinganoptimizeddesign intheveryrstcut. 37

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Theestimationtechniquesproposedsofartreattheamplitu deandwidthofthenoise pulseastheobjectivefunctions.Ourapproachdiersfromt heminthatwetakeahigh-level viewoftheproblemandtreatallpossiblecrosstalkphenome noncollectivelyas crosstalk eects .Basedonthenumberofcrosstalkeventsoneverylineoftheb us,weevaluatea probabilitythatindicatestheamountofcrosstalkactivit yonthatline.Theadvantageof ourapproachisthatitgivesthedesigneranideaastowhichb uslinesaremoresusceptible tocrosstalk.Basedonthisinformation,buslineswhichare highlysusceptibletocrosstalk maythenbereorderedorencoded[68][72][1][69][57].Formalstatementoftheproblem :Givenonlytheword-levelstatisticsofthedataona systembus,theobjectiveistoanalyticallyestimatethecr osstalksusceptibilityofeachbus line.Thetechniqueshouldbeindependentofthelengthofda tastreamsonthebussothat theestimationprocesstakesaconstanttime,irrespective ofthedatastreamlength. 3.2Problemformulation Awirehavingcouplingcapacitancewithanotherwiremaybet reatedaseithera victim oran aggressor withrespecttotheotherwire.Ifitisavictim,itmeansthat transitions ontheotherwirewilladverselyaectthesteadystateaswel lastransitionsonit.Ifitis anaggressor,itmeansthatitwillaecttheotherwireadver sely.Figure3.3[1]showsthe victimwire V entrappedbetweentheaggressors A1 and A2 .However,thewire V could alsoactasanaggressorforboth A1 and A2 Thecoupledcapacitancebetweenwireshasaneectonbothth edelayandpower dissipationofthevictimline.Ifthevictimisatasteady-s tatevalueandtheaggressor isswitching,itproducesaspikeonthevictiminthedirecti oninwhichtheaggressor isswitching.Thishastheeectofunwantedpowerdissipati ononthevictimline.In particular,ifthevictimdevelopsaspikebelowitslogicle vel`0' V L oraboveitslogic level`1' V H ,itisreferredtoasthe bootstrapnoise .Ifthevictimisswitchinginthesame directionastheaggressor,thelatterreinforcesthevicti m'stransition,therebyhasteningit. 38

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Table3.1.Possiblecrosstalkeects SignalTransitiononAggressor SignalTransitiononVictim ResultantCrosstalkeect 0 1 0 0 Upwardspike 1 0 0 0 Bootstrapspike 0 1 1 1 Bootstrapspike 1 0 1 1 Downwardspike 0 1 0 1 Victransitionhastened 1 0 0 1 Victransitiondelayed 1 0 1 0 Victransitionhastened 0 1 1 0 Victransitiondelayed Voltage Time Cg = 44.4fF, Cx = 82.3fF Victim Aggressor Vl = 0V Vh = 1V 4 3 2 1 Figure3.1.Crosstalkspikeeectsonvictims 39

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Voltage Time 4 3 2 1 Cg = 44.4fF, Cx = 82.3fF Vl = 0V Vh = 1V Victim Aggressor Figure3.2.Crosstalkdelayeectsinvictims Thiseectisoftenignoredunderthesimplisticassumption thatifadjacentlinesswitchin thesamedirection,thecouplingcapacitancebetweenthemi szero[74].However,thiscould underestimatetheactualdelayofthevictim[74].Ifthevic timisaninputtoalatch,this eectwouldcauseviolationinthe holdtime requirementsofthelatch,therebyupsettingthe nextstateofthesequentialcircuit.Again,ifthevictimis switchinginadirectionopposite tothatoftheaggressor,thetransitionofthevictimgetsop posedbytheaggressor,thereby delayingit.Thiswouldalsoaectthetimingofthecircuita dversely.Table3.1givesa summaryofthepossiblecrosstalkeects.InFigure3.1,spi kes2and3indicatebootstrap noiseonthevictimwhile1and4indicateupwardanddownward spikesrespectively.In Figure3.2,1and4indicatehasteningofthevictim'stransi tionswhile2and3indicatethe delayingofthevictim'stransitions.Theseplotswereobta inedusingHSPICEbysimulating acircuitwithoneaggressorandonevictim. 40

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Keycontributionsofourwork: Themaincontributionsofourworkareasfollows: 1.Weaddresstheintra-buscrosstalkproblematthehigh-le vel.Givenonlyword-level statisticsofsignals,weproposeastatisticaltechniquet hatestimatestheamountof crosstalksuchsignalscauseonthelinesofasystembus. 2.Weproposeanewmetric,namelythe probabilityofcrosstalkevents foreachlineof thebus. 3.Forvericationoftheproposedtechnique'sresultswith physical-levelresults,we proposeastream-basedtechniquethatcomputesthetotalnu mberofcrosstalkevents inadatastreamthatisaninputtothebus. 4.UsingdetailedHSPICEsimulation,weshowthatthestream -basedtechniqueisexactlyasaccurateandfasterthanHSPICE. 5.Theproposedstatisticaltechniqueisindependentofdat astreamlengths.Thus,the runtimesareconsiderablyreducedwhileaccuracyismainta ined. Theproposedstream-basedtechniquethatweuseforverica tionsimplycountsthe numberofcrosstalk-producingpatternsintheinputdatast ream.Thetotalnumberof crosstalkeventsoneachlineofthebusgivesusanestimateo ftheprobabilityofsuch eventsonthatline.Ontheotherhand,theproposedstatisti caltechniquereliesonlyon word-levelstatisticalparametersoftheinputdatastream ,namelythemean,standard deviation,andlag-1temporalcorrelation,tocomputeabit -levelcrosstalkprobabilityfor eachlineofthebus.Hence,itisindependentofthedatastre amlength.Theproposed statisticaltechniquehasbeencurrentlyappliedtoestima teintra-buscrosstalk. 3.3Proposedtechnique1:stream-basedcrosstalkeventest imator Theprevioussectionillustratesthatthecrosstalkeects ariseduetotransitionsofthe aggressors withrespecttothe victim wires.Sinceweconsiderintra-buscrosstalk,itis reasonabletoassumethatallthelinesofthebusareclocked atthesameinstant.Hence, 41

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Cg Cg Cg Cx Cx Aggressor A1 Victim V Aggressor A2 Figure3.3.Aggressor-victimsimulationcircuit n n n n n n n n n n n n n n n n n n VAA2A1 V EdgeMiddle Figure3.4.Checkingbittransitionsforcrosstalkpattern s theaggressor-victimtransitionstranslatetospecic bitpatterns intheinputdatastream tothebus. Theproposedstream-basedestimatortracestheinputdatas treamforpatternswhich willcausecrosstalk.Thetechniquecanbeappliedtoanydat aenvironment.The middle linesinthebussuercrosstalkeectsfromboththeiradjac entaggressorswhilethe edge lineshaveonlyoneaggressorwhichisresponsibleforcross talk.Thus,themiddlebitsof thedatawordloadedontothebusateveryinstant,arecompar edtothesamebitsofthe previousdatawordingroupsofthree,namely A 2 V A 1 .Ontheotherhand,theedgebits (boththeMSBaswellastheLSB)ofthecurrentwordarecompar edtothepreviousword ingroupsoftwonamely VA fortheMSBand AV fortheLSB.Figure3.4illustratesthe comparisons. Theprocedurethencountsthenumberofbittransitionsonth eaggressorsthatcontributetowardscrosstalkseparately,foreverylineonthe bus.Thus,attheendofthe procedure,wehavethetotalnumberofcrosstalkeventsonev erylineonthebus.Sincethe 42

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Table3.2.HSPICEvsstream-basedruntimes Datawordsize(bits) Length HSPICE(time) Stream-based(time) 8 1000 32s 25s 8 3000 129s 70s 16 1000 102s 26s 16 2000 147s 69s lengthofthedatastreamisknown,weobtaintheprobability p ofacrosstalkeventonany buslineusingthefollowingequation: p = n l (3.1) where n isthenumberofcrosstalkeventsand l isthelengthofthedatastream. TheaccuracyofthismethodiscomparedagainstdetailedHSP ICEsimulation.Thespice netlistofthe m -bitbusissimulatedusingthesameinputdatastream.Theto talnumberof crosstalkeventsreportedoneachlineofthebusbyHSPICE,i smatchedwithourapproach. Asexpected,thereisanexactone-to-onecorrespondencein thetotalnumberofcrosstalk eventsobtainedoneachlineofthebusbythetwomethods.How ever,ourapproachisfaster thanHSPICEbecauseitreadsthecrosstalkeventsdirectlyf romthedatastreamwithout simulatingit.Table3.2comparestheruntimesofthetwoapp roachesfordatastreamsof variouslengths,generatedusingARMAmodels[11].Allexpe rimentswereperformedona SunUltra2dual-processorworkstation.3.4Proposedtechnique2:statisticalenumerativeapproac hforcrosstalkevent estimation Thedrawbackofthestream-basedtechniqueisthatitisdepe ndentonthelengthof thedatastream.Toalleviatethis,weproposeastatistical techniquethatcomputesthe crosstalkprobabilityoneverylineofthebus,basedonthes tatisticalparametersofthe datastream x ( n ).Thismakesitindependentofthedatastreamlength. Theproposedapproachmakesuseofsomestatisticalparamet ersofthedatastream whicharemathematicallydenedasfollows: 43

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1.Meanofthestream x(n) = E [ x ( n )](3.2) 2.Standarddeviationofthestream = p E [ x 2 ( n )] E 2 [ x ( n )] = p E [ x 2 ( n )] 2 (3.3) 3.Temporal(lag-1)correlationofthestream:Thisindicat eshow,atanyinstant,the currentvalue x ( n )inthestreamisrelatedtothevalue x ( n 1)atthepreviousinstant andisgivenby: = E ( x ( n ) )( x ( n 1) ) E [( x ( n ) ) 2 ] = E [ x ( n ) x ( n 1)] 2 2 (3.4) Letusassumethatthesignal x ( n )onthebushasanormaldistribution.Thereis, however,norestrictiononthedistributionof x ( n ).Wejustassumethenormaldistribution asageneralcase[12].Typically,theprobabilitydistribu tionof x ( n )canbeestimatedfrom theARMAsignalgenerationmodels.Inthiswork,weassumeth atthedistributionof x ( n )isknownbeforehand.Inthecontextofhigh-levelpowerest imationusingword-level statistics,Ramprasadet.al.[11]andSatyanarayanaet.al [12]makesimilarassumptions aboutthedataenvironments. Theprobability p i ofthe i thbit b i inthedatawordistheprobabilitythatthe i thline ofthebusisa1.Thisisgivenby: p i = Pr ( x ( n ) 2 i ) = X j 2 i 1 p 2 e ( j ) 2 = 2 2 (3.5) where i isthesetofallelementsin whose i thbitis1. 44

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Fromequation4,itisevidentthatthetemporalcorrelation of x(n) isdependentonthe covariance E [ x ( n ) x ( n 1)]termwhichisastatisticalparameter,generallyindepe ndentof themeanandvarianceofthestream.Asanexception,iftheda tavaluesinthestream arerandom,thenthecovariancetermcanbeexpressedasasqu areofthemean.But,for ahighlycorrelateddatastream,thecovariancecannotbees timatedfromthemeanand varianceofthedata. Itisthusdiculttoaccuratelyestimatethetemporalchara cteristicofthedatafrom otherword-levelstatistics.Further,itiscumbersometoc omputethesamefrombit-level information.Hence,weemploya concatenation procedurewhichenablesustocontinue workattheword-level,bytransformingthetemporalcharac teristicatthebit-leveltothe spatialcharacteristicsoftheconcatenatedstreams. Letusassumethattheon-chipbusis m bitswide.Correspondingly,thereare m bits inthedataloadedontothebusduringsuccessiveclockcycle s.Ifthedatavalueatevery instant x ( n )isconcatenatedwiththevalueduringthepreviousinstant x ( n 1),weobtaina compound dataword X ( n )ofwidth2 m .Figure3.5depictstheformationofthecompound wordwhen m is8bitswide. Theconcatenateddatastream X ( n )canthenbeexpressedintermsofthecomponent streams x ( n 1)and x ( n )usingthefollowingequation: X ( n )=2 m x ( n 1)+ x ( n )(3.6) Wederiveanalyticalequationstocomputethemeanandstand arddeviationofthe compoundstream X ( n )fromthestatisticsoftheoriginalstream x ( n )asfollows. 45

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x(n): m_x, s_x, r_x X(n): m_X, s_X w = 2m-bits x(n-1): m_x, s_x, r_x w = m-bits w = m-bitsFigure3.5.Concatenation X ( n )=2 m x ( n 1)+ x ( n ) E [ X ( n )]=2 m E [ x ( n 1)]+ E [ x ( n )] X =2 m x + x =(2 m +1) x (3.7) 2 X = E [ X 2 ( n )] E 2 [ X ( n )] = E [2 2 m x 2 ( n 1)+ x 2 ( n )+2 m +1 x ( n 1) x ( n )] 2X = E [2 2 m x 2 ( n 1)+ x 2 ( n )+2 m +1 x ( n 1) x ( n )] 2 2 m E 2 [ x ( n 1)] E 2 [ x ( n )] 2 m +1 E [ x ( n 1)] E [ x ( n )] =2 2 m [ E [ x 2 ( n 1)] E 2 [ x ( n 1)]]+ E [ x 2 ( n )] E 2 [ x ( n )] +2 m +1 [ E [ x ( n 1) x ( n )] 2 ] =(2 2 m +1) 2 x +2 m +1 [ x 2 x + 2x 2x ] =(2 2 m +1+2 m +1 x ) 2 x X = x p 2 2 m +1+2 m +1 x (3.8) 46

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Fromequation(3.6),weobservethatconcatenationisaline aroperationinvolvingamultiplicationandanadditionoperation.Anylinearoperatio nsonnormaldistributionsresults inanothernormaldistributionwithadierentmeanandstan darddeviation[75][76].Thus, theconcatenateddatastream X ( n )hasanormaldistributionwithmean X andstandard deviation X .Wethenutilizetheseparameterstocomputethecrosstalkp robabilityfor themiddlelinesofthebus.3.4.1Crosstalkformiddlelines Weassumeonlyrstordercrosstalkeectsinourworkinorde rtodemonstratethe technique.Thismeansthatanyvictimisaectedbyonlyitsi mmediatelyadjacentaggressors.Thus,withinthebus,therearetwoaggressors A2 and A1 aectinganyvictim V in themiddle. A2 and A1 areimmediatelyadjacentto V inthesequence A2VA1 .However, theproposedtechniquecaneasilybeextendedtoincorporat ehigherordereects.Forrst ordereects,thevictimlinesexperiencecrosstalkwhenei theroneoftheaggressorsswitch whiletheotheroneissteadyorwhenboththeaggressorsswit chinthesamedirection. Oppositetransitionsonadjoiningaggressorsofanyvictim linenullifythecrosstalkeect onthevictim. Theconcatenatedword X ( n ) (b15-b0) has two crosstalk windows ,asshowninFigure3.6. Therstisinthe x ( n )regionwhilethesecondisinthe x ( n 1)region.Itcanbeseenthat thesetwowindowsarealwaysseparatedbyaconstantdistanc e,equaltothewidth m of thebus.Theconcatenated X ( n )isreferredtoasa crosstalktemplate whichisdenedasa 2m -bitwordwhere six ofthebitsaresubstitutedwithagivencrosstalkpatternof interest. Theproposedtechniqueinvolvessubstitutingcrosstalkpa tternsinthecurrentcrosstalk windows.Forrstordercrosstalkeects,thecrosstalkpat ternsareoflength6bits,with eachwindowhaving3bits.Atypicalcrosstalkpatternis 001111 sinceitcausesaggressor A2 toswitchfrom`0'to`1'whileaggressor A1 isxedat`1'andvictim V isswitchingfrom `0'to`1'.Thispatternhastheeectofhasteningthetransi tionon V .Similarly, 101001 is acrosstalkpatternwhile 110011 isnot.Eachvalidcrosstalkpatternofinterestisreferred 47

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x(n-1)x(n) b8 b7b1 b2 b3 b4 b5 b6 b14b13b12b11b10b9 001111 b0 Crosstalk template instance Crosstalk templates for 8-bit bus b15 Figure3.6.Bit-levelcrosstalktemplatesfor8-bitbus toasa crosstalktemplateinstance .Forrst-ordercrosstalkeectsoneverybusline,there are40templateinstanceswhichcoverallpossiblecrosstal keectslistedinTable3.1. Oncethecrosstalkwindowsarelledwithagivencrosstalkp attern,theremainingbits in X ( n )areiterativelylledforallpossiblecombinations.Each ofthoseword-levelvalues of X ( n )isacrosstalk-producingvalueforthecurrenttemplatein stance. Next,wecomputetheprobabilitythatsuchcrosstalk-produ cingvaluesarepresentinthe datastream.Theprobabilitythatadiscretevaluedvariabl e X ( n )assumesacertainvalue inagivenprobabilitydistributionisobtainedbysubstitu tingthevalueintheprobability distributionfunctionitself[75].Thus,intheconcatenat ed,normallydistributeddatastream X ( n ),theprobabilitythataparticularcrosstalk-producingv alue j ispresent,isgivenby p j = P ( X = j )= 1 X p 2 e ( j X ) 2 = 2 2 X (3.9) Thevaluesofthemean X andstandarddeviation X of X ( n )areanalyticallycomputed fromequations(3.7)and(3.8).Thus,forxedpositionsoft hecrosstalkwindows,say b0-b2 and b8-b10 ,weareabletoevaluatetheprobabilityofcrosstalk-produ cingvaluesbysumming uptheprobabilitiesofallcrosstalk-producingwordsin X ( n )foreverycrosstalktemplate 48

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Figure3.7.Proceduralrow instance.Thisgivestheprobabilitythatthebit b1 inthe m -bitdatawordexperiences crosstalk.Mathematically, p b 1 = X j 2 templ i nst p j (3.10) Thecrosstalkwindowsthenslideonepositiontotheleftnam ely b1-b3 and b9-b11 to similarlyevaluatethecrosstalkprobabilityofthebit b2 .Thisprocedurekeepsrepeating untilthewindowsreachtheMSBpositions,asshowninFigure 3.6.Aftertheprocedureis complete,weobtainacrosstalkprobabilityforeachofthem iddlelinesinthebus.Figure3.7 givesasummaryofthetechnique.3.4.2Crosstalkforedgelines Asstatedpreviously,theMSBandLSBlinesofthebushaveonl yoneaggressoreach. Theyexperiencecrosstalkwhenevertheiraggressorunderg oesatransition.Thetransition couldbeineitherdirection.Iftheedgelineisinasteadyst ate,itwilldissipatepowerdueto crosstalkspikes.Ifitisswitching,itwillexperienceear lytransitionsordelaysdependingon whetheritisswitchinginthesameorintheoppositedirecti onastheaggressor,respectively. 49

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Table3.3.Dataenvironments Bit-width Environment ARMAequation 8 SIG1 x(n)=50 r (n)-10 8 SIG2 x(n)=30 r (n)+0.5x(n-1) 8 SIG3 x(n)=75 r (n) 8 SIG4 x(n)=50 r (n)+0.7x(n-1) 10 SIG1 x(n)=250 r (n)+100 10 SIG2 x(n)=200 r (n)+0.5x(n-1) Thus,theprobabilityofcrosstalkontheedgewiresisthesa measthetransitionprobability oftheiraggressors.From[11],thetransitionactivityoft he i thbitisgivenby t i =2 p i (1 p i )(1 i )(3.11) where p i and i arethebitprobabilityandbitcorrelationofthe i thbitrespectively.Both theseparameterscanbeestimatedusinganalyticaltechniq uespresentedin[11].Thus, usingequation3.11,weobtainthecrosstalkprobabilityof theedgebitsfromthewordlevel statisticsofthedatastream.3.5Experimentalresults Astheproposedstream-basedestimationisasaccurateandf asterthanHSPICEin termsofmeasuringcrosstalkevents,wereplaceHSPICEwith ourstream-basedestimator asthebasisforcomparingthequalityofthesubsequentlypr oposedstatisticalcrosstalk estimators. Table3.3showsthedataenvironmentsmodeledusingARMAmod els.SuchARMA modelsareoftenusedtorepresentspeechandvideosignals. Theproposedapproachis generalenoughtohandlevariousdataenvironments.Thisme ansthatitwillworkonall datastreamsfromsuchenvironments.Thewhitenoisefactor r (n)hasastandardnormal distribution. Tables3.4and3.5comparethecrosstalkprobabilitiescomp utedbythestream-based andstatisticalenumerationproceduresfor m =8.Themaximumerrorproducedis26% 50

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Table3.4.Crosstalkprobabilityfor8-bitbus-SIG1andSIG 2 SIG1 SIG2 Busline Str-based Stat.enum Err(%) Str-based Stat.enum Err(%) 1 0.50 0.50 0.0 0.50 0.50 0.0 2 0.62 0.61 1.6 0.62 0.62 0.0 3 0.62 0.61 1.6 0.62 0.63 1.6 4 0.61 0.62 1.6 0.62 0.61 1.6 5 0.62 0.61 1.6 0.62 0.58 6.8 6 0.61 0.57 7.0 0.63 0.50 26.0 7 0.62 0.63 1.5 0.62 0.55 12.7 8 0.32 0.32 0.0 0.11 0.11 0.0 Averageerror:1.9%6.1% Table3.5.Crosstalkprobabilityfor8-bitbus-SIG3andSIG 4 SIG3 SIG4 Busline Str-based Stat.enum Err(%) Str-based Stat.enum Err(%) 1 0.51 0.51 0.0 0.49 0.49 0.0 2 0.62 0.60 3.2 0.63 0.61 3.1 3 0.62 0.60 3.2 0.62 0.60 3.2 4 0.62 0.60 3.2 0.63 0.61 3.1 5 0.60 0.60 0.0 0.61 0.61 0.0 6 0.62 0.60 3.2 0.56 0.60 7.1 7 0.58 0.60 3.4 0.56 0.60 7.1 8 0.46 0.46 0.0 0.34 0.34 0.0 Averageerror:2.0%2.9% whiletheaverageerrorislessthan7%.Table3.6comparesth ecrosstalkprobabilitiesfor m =10.Theaverageerrorislessthan6%. Therun-timesofthetwoproposedapproachesarecomparedin Table3.7.Thestatistical enumerativeapproachisshowntobeconsiderablyfastertha nthestream-basedapproach. Thisisbecausethestatisticalenumeratorisindependento fthelengthofthedatastream whiletheexecutiontimeofthestream-basedapproachincre asesindirectproportiontothe lengthofthedatastream. 51

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Table3.6.Crosstalkprobabilityfor10-bitbus-SIG1andSI G2 SIG1 SIG2 Busline Str-based Stat.enum Err(%) Str-based Stat.enum Err(%) 1 0.48 0.49 2.0 0.49 0.50 2.0 2 0.61 0.63 3.2 0.61 0.62 1.6 3 0.61 0.62 1.6 0.61 0.62 1.6 4 0.61 0.62 1.6 0.62 0.62 0.0 5 0.61 0.62 1.6 0.61 0.61 0.0 6 0.61 0.62 1.6 0.61 0.62 1.6 7 0.60 0.62 3.2 0.61 0.61 0.0 8 0.61 0.59 3.4 0.62 0.56 10.7 9 0.60 0.59 1.7 0.61 0.57 7.0 10 0.38 0.43 11.6 0.43 0.33 30.3 Averageerror:3.2%5.5% Table3.7.Stream-basedestimatorvsstatisticalenumerat orruntimes Datawordsize(bits) Length Stream-based(time) Stat.enumerator(time) 8 450 14.45s 7.7s 8 3000 1min.17s 7.2s 8 5000 2min.13s 7.5s 8 6500 3min.16s 7.8s 10 9500 4min.22s 3min.10s 10 14500 6min.37s 3min.11s 52

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3.6Conclusions Inthischapter,wepresentedahigh-level,statisticalenu merativetechniqueforfast estimationofthecrosstalkeectswithinasystembus,usin gtheprobabilityofcrosstalk eventsasourmetric.Wecomparedittoaproposedstream-bas edtechniquethatwasshown tobefasterthanHSPICE,withoutanylossinaccuracy.Altho ughthespeedupobtainedin thestatisticalestimationprocessissignicant,thealgo rithmiccomplexityoftheestimator, withrespecttothebus-width,isexponential.Thefollowin gchapteraddressesthisissue. 53

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CHAPTER4 IMPROVINGTHECOMPLEXITYOFTHESTATISTICALESTIMATION Thestatisticalenumerativecrosstalkestimatordiscusse dinthelastchaptersuersfrom lackofscalabilityduetoitshighcomplexitywithrespectt othebus-width.Inordertosolve thecomplexityissue,weintroducesomenovelmodications toit.Thischapterdiscusses astatisticalnon-enumerativetechniquethathaslinearti mecomplexitywithrespecttothe bus-width.Weachievethelinearcomplexitybyresortingto :(1)manipulationofthedata streamtomakethecrosstalk-producingvaluescontinuousa nd(2)samplingthedistribution functionandstoringitasalookuptable.Experimentalresu ltsfordatastreamsfrom dierentdataenvironmentsarepresented,comparedagains tthestream-basedapproach. Averageerrorsoflessthan15%areobtainedforbus-widthsr angingfrom8bto32b.Further, duetothelinearizationofthecomplexity,theexecutionti mesarereducedbytwoordersof magnitudeascomparedtoHSPICE.4.1Introductionandproblemformulation Themodicationsthataremadetothestatistical enumerative processtomakeit nonenumerative arestatedasfollows: 1.Weusethe circularrightshift operationtochangethepositionofthecrosstalktemplatesintheconcatenateddataword.Suchanoperationhast heeectofconverting disjointvaluesintheenumerativeprocessintocontinuous values.Thesummationof disjointvaluesintheenumerativeprocessisreducedtoasi ngledeniteintegral. 54

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1 10100A2 A1 Vx(n-1)x(n)X(n) xx Figure4.1.Concatenation 2.Further,weintroducea sampling techniquetoevaluatedeniteintegralsfordiscretevaluedrandomvariables.Thislinearizesthetimecomplexi tyoftheestimationprocess withrespecttothebus-width. 4.2Proposedstatisticalnon-enumerativeapproach Asinthecaseofthestatisticalenumerativeestimationpro cess,weassumethatthe signal x ( n )onthebushasanormaldistributionwhichisknown apriori [11][12].Thesignals aregeneratedusingARMAequations.Besides,toavoiddeali ngwithbit-levelstatistics, thetemporalcharacteristicsofthedatastreamaretransfo rmedtospatialcharacteristics, usingthe concatenation technique,asbefore.Theword-levelstatisticsoftheconc atenated datastreamarederivedanalytically.Themainequationspe rtainingtotheprobability distributionandconcatenationofconsecutivedatawords, arereproducedinequations4.2 ?? Theprobability p i ofthe i thbit b i inthedatawordonthebusistheprobabilitythat the i thlineofthebusisa1.Thisisgivenby: p i = Pr ( x ( n ) 2 i ) = X j 2 i 1 p 2 e ( j ) 2 = 2 2 (4.1) where i isthesetofallelementsin whose i thbitis1. 55

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b2 b1 b0 b10 b9 b8 b15 b14 b13 b12 b11 b7 b6 b5 b4 b3 b10 b9 b8 b15 b14 b13 b12 b11 b7 b6 b5 b4 b3 b2 b1 b0 b15 b14 b13 b12 b11 b10 b9 b8 b7 b6 b5 b4 b3 b2 b1 b0 Figure4.2.Continuouscrosstalkwindowsusingcircularri ghtshift X ( n )=2 m x ( n 1)+ x ( n )(4.2) X =(2 m +1) x (4.3) X = x p 2 2 m +1+2 m +1 x (4.4) Theconcatenateddatastreamretainsthenatureoftheproba bilitydistributionofthe originalinputdatastreamtothebus.Thestatisticsofthec oncatenateddatastream X ( n ) namely,mean X andstandarddeviation X ,areutilizedinthenextstepofthealgorithm. Toscalethecrosstalkestimationsolutionecientlyforla rgerbus-widths,thenextstep ofthealgorithminvolvesshiftingthedisjointcrosstalkw indowstotheMSBpositionsso thattheyareadjacenttooneanother,asshowninFigure4.2. Thisisdoneusingthe CircularRightShift(CRS) operationwhichobeysthefollowingequation: x 0 ( n )= b x ( n ) = 2 c +2 m 1 [ x ( n ) mod 2](4.5) 56

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where x 0 ( n )isobtainedbyshifting x ( n )oncetotherightinacircularfashion.From equation4.5,weobservethatthe CRS operationalsopreservesthenormalpropertiesof thedistributionbecauseofitslinearnature. Each CRS operationcausesthestatisticsofadatastreamtochange.U singtheabove CRS equation,wederiveanalyticalequationsthatrelatetheme anandstandarddeviation oftheshifteddatastream x 0 ( n )tothoseoftheoriginalstream x ( n )asshown: E [ x 0 ( n )]= E b x ( n ) = 2 c +2 m 1 E [ x ( n ) mod 2] x 0 = x 2 +2 m 1 (4.6) 2 x 0 = E [ x 0 2 ] 2x 0 = E [ x ( n ) 2 4 +2 2( m 1) [ x ( n ) mod 2] 2 +2 m 1 x ( n )[ x ( n ) mod 2]] 2x 4 2 m 1 x 2 2( m 1) 2 2x 4 2 m 1 x 2 2( m 1) 2 = E [ x ( n ) 2 ] 4 +2 2( m 1) +2 m 1 x 2x 4 2 m 1 x 2 2( m 1) 2 = 2 x 4 +2 2( m 1) ( 2 )(4.7) where = E[x(n)mod2] isthebitprobabilityofthecurrentLSBin x ( n ). ThisCRSoperationisperformedintwostagestocreateconti nuouscrosstalkwindows. Itisrstappliedtothelefthalfof X ( n )togetamodied2 m -bitvalue X 1 ( n )Now,theCRS operationisagainperformedon X 1 ( n )togetthetransformedvalue X 2 ( n ).Thismakesall thebitsinagivencrosstalkpatternadjacenttoeachothera ndlocatedinthe MSB region 57

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**00011011 b7b6b5b4b3b2b1b0 11 131139 3 X(n) 1 00001(a)Enumerativeb1b0 011000 **0 1 0 0 1 1 1 0 96979899X (n)2b2 b7b6b5b4b3(b)Non-enumerative Figure4.3.Enumerative&non-enumerativetechniquesfora 4-bitbuswithtemplateinstance000011andvictimb1of X 2 ( n ).Consequently,dispersedvaluesintheoriginal X ( n )maptocontinuousvaluesin X 2 ( n ). Considera4-bitbusasanexample.Thecompoundword X ( n )is8-bits( b7-b0 )wide. Now,ifbits b6-b4 =`000'andbits b2-b0 =`011',itcorrespondstoatransitionthatcauses crosstalkon b1 .Bysubstituting`00'forbits b7b3 ,weobtainthevalue3whichrepresentsa crosstalkproducingtransitionfor b1 .UsingtheCRStechnique,wenowshiftthecrosstalk patterntotheMSBpositionofthe8-bitbus.Thepatternnowr eads`011000'.Bysubstituting`00'forbits b1b0 ,weobtainthevalue96.Thus,thedisjointvalues f 3,11,131,139 g in X ( n )maptothecontinuousvalues f 96,97,98,99 g in X 2 ( n ).AsshowninFigure4.4, exhaustiveenumerationofvalues v1,v2,v3 ,and v4 reducestotheintegralbetweenlimits l1 and l2 with l 1=96and l 2=99.Figure4.3illustratestheexamples. Thismodicationreducesthecomplexityofthealgorithmfr omexponential(inthe disjointcase)tolinear(inthecontinuouscase)withrespe cttothebus-width m 4.2.1Evaluationofthedeniteintegralusingsampling Forlargebus-widths,theboundsofthedeniteintegralsar efarapart.Sincethewordlevelvaluesarediscreteinnature,weproposea sampling techniquetoevaluatetheintegrals insuchcases.Thisprovidesafastandaccuratesolution. 58

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m1 m2 s1 -s1 -s2s2 v1 v2v3 v4l1 l2 Probability distributionProbability distribution Figure4.4.Enumerationtointegraltransformation Eachintervalcorrespondingtoanintegralissampledaspec icnumberoftimes.Each valueobtainedbysubstitutingthesampleintotheprobabil itydistributionfunctionisstored ina look-uptable .Theintervalisnowsplitupintosub-intervalswhosewidth isgivenby: w si = ub lb +1 n (4.8) where w si isthewidthofeachsub-intervalandtheintegralisbounded by[ lb,ub ]and sampled n times.ThisisillustratedinFigure4.5.Thus,eachsub-int ervalisboundedby valueswhicharestoredinthelook-uptable.Weevaluatethe integralforeachsub-interval bytakingtheproductofthemedianforthesub-intervalandw idth w si .Ifthevaluesstored inthelook-uptableare v 1 v 2 v 3 ,..., v n ,theintegral I j forthej th sub-intervalisgivenby: I j = v j + v j +1 2 w si (4.9) Theintegralsfortheremainingsub-intervalsarealsoeval uatedinasimilarmanner.We thencomputetheintegral I int fortheinterval[ lb,ub ]bysumminguptheintegralsforall thesub-intervals.Thus, I int = n 1 X j =1 I j (4.10) 59

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v2 v1vn LBUB w(si) 1/2 (v1 + v2) Figure4.5.Thesamplingtechnique Table4.1.Dataenvironments Bit-width Dataenv ARMAequation 8 SIG1 x(n)=75 r (n)+200 16 SIG2 x(n)=250 r (n)+56*10 3 32 SIG3 x(n)=10 6 r (n)+0.5x(n-1)+5*10 8 Foreachofthemiddlelines,thecrosstalkprobabilityisco mputedbysummingupsuch integrals.Fortheedgelines,thecrosstalkprobabilityis obtaineddirectlyfromthetransition activityoftheiraggressors,usingEquation(3.11).Theno n-enumerativeprocedurerowis illustratedinFigure4.6.4.3Experimentalresults Wecomparetheproposednon-enumerativestatisticalcross talkestimationtechnique withthestream-basedtechniqueintermsofbothaccuracyan dspeedfordierentdata environments. Table4.1showsthedataenvironmentsmodeledusingARMAmod elsasbefore.The proposedapproachisgeneralenoughtohandleanydataenvir onment.Thismeansthatit willworkonalldatastreamsfromsuchanenvironment.Thewh itenoisefactor r (n)hasa standardnormaldistribution. 60

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sampling. Acculate p in P within [LB, UB] with p
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Table4.3.Crosstalkprobabilityfor8-bitbus-SIG1&reala udiodata SIG1 Realaudiodata Busline Str-based NET Str-based NET 1 0.51 0.51 0.43 0.41 2 0.62 0.58 0.52 0.50 3 0.63 0.59 0.55 0.50 4 0.65 0.58 0.48 0.44 5 0.62 0.57 0.43 0.43 6 0.63 0.57 0.44 0.43 7 0.51 0.69 0.50 0.58 8 0.49 0.49 0.32 0.37 Tables4.2-4.5comparethecrosstalkprobabilitiesascomp utedbythestatisticalapproachagainstthoseobtainedfromthestream-basedestima torforbus-widthsrangingfrom 8bitsto32bits.Theaverageerrorfortheentirebusfor m =8bis9.5%whilefor m =16b and m =32b,theaverageerrorsare5.9%and14.9%respectively. BesidestheARMAmodels,wetesttheproposedapproachusing realaudiodatafroma humanvoice.Theaudiowasrecordedusingthe audiotool utilityinUNIX.Theresultsare showninTable4.3.Theaverageerroris7.4%. Itmaybenotedthatalthoughtheprobabilityerrorinline25 forthe32-bitbusisvery high,itdiersonlyintheseconddecimalplace.Inpractice ,ithasonly9%chanceof crosstalkwhichweestimatetobenegligible. Theruntimesfortheproposednon-enumerativetechniquear ecomparedtothoseof thestream-basedestimatorfordierentbus-widthsinTabl e4.6.Itistobenotedthat withincreaseinthedatastreamlength,thedierenceinthe runtimesbecomesevenmore signicant. Increasingthenumberofsamplesincreasestheaccuracyasw ellastheruntimes.Itis observedthatbeyondacertainnumberofsamples,theincrea seinaccuracyisinsignicant ascomparedtotheruntimes.Hence,thenumberofsamplestob eusedforeachinterval shouldbediscreetlyselected.Table4.7showstheeectsof thenumberofsamplesonthe runtimes. 62

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Table4.4.Crosstalkprobabilityfor16-bitbus Busline Stream-based Stat.estimator Err(%) 1 0.53 0.53 0.0 2 0.61 0.70 14.7 3 0.66 0.70 6.1 4 0.63 0.69 9.5 5 0.63 0.69 9.5 6 0.62 0.68 9.7 7 0.62 0.68 9.7 8 0.65 0.68 4.6 9 0.60 0.75 25.0 10 0.51 0.54 5.9 11 0.46 0.46 0.0 12 0.15 0.15 0.0 13 0.00 0.00 0.0 14 0.00 0.00 0.0 15 0.00 0.00 0.0 16 0.00 0.00 0.0 Averageerror:5.9% *++ + + x2 x1 x4 x3x5 r5 yout r7 r6 r4 r3 r2 r1 r0 x9 x10 x8 x7 x6 Figure4.7.FIRlter 63

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Table4.5.Crosstalkprobabilityfor32-bitbus Busline Stream-based Stat.estimator Err(%) 1 0.31 0.27 12.9 2 0.50 0.52 4.0 3 0.59 0.46 22.0 4 0.65 0.48 26.2 5 0.62 0.49 20.9 6 0.61 0.49 19.7 7 0.64 0.50 21.8 8 0.64 0.50 21.8 9 0.64 0.50 21.8 10 0.61 0.50 18.0 11 0.62 0.47 24.2 12 0.62 0.49 20.9 13 0.61 0.49 19.7 14 0.62 0.50 19.3 15 0.59 0.50 15.2 16 0.63 0.50 20.6 17 0.63 0.50 20.6 18 0.64 0.50 21.9 19 0.60 0.50 16.7 20 0.64 0.50 21.9 21 0.57 0.50 12.3 22 0.53 0.44 17.0 23 0.35 0.47 34.3 24 0.13 0.16 23.0 25 0.09 0.01 88.9 26 0.00 0.00 0.0 27 0.00 0.00 0.0 28 0.00 0.00 0.0 29 0.00 0.00 0.0 30 0.00 0.00 0.0 31 0.00 0.00 0.0 32 0.00 0.00 0.0 Averageerror:14.9% Table4.6.Stream-basedestimatorvsstatisticalestimato rruntimes Bus-width Length Stream-based Statestimator 8b 1000 22.4s 0.4s 16b 1000 24.3s 1.2s 32b 1000 33.0s 0.5s 64

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Table4.7.Eectofsamples(s)onruntimes Bus-width s=1000 s=5000 s=50000 16 1.2s 2.6s 10.0s 32 0.5s 1.7s 15.0s Wedemonstratetheapplicationofthenon-enumerativestat isticalestimatortocompute thecrosstalkprobabilitiesofeachlineoneachedgeofani te-impulseresponse(FIR)lter. Thedata-rowgraphfortheFIRlterisshowninFigure4.7.Ea chedgeofthelter isan8-bitbusandtheproposedestimatorisrunusingthewor d-levelstatisticsonthat edge.Thestatisticsthemselvesarepropagatedusingthete chniqueproposedbyRamprasad et.al.[11].Thecrosstalkestimateforeachlineofanedgei scomparedagainstthestreambasedprogram.Forsimplicity,onlytheaverageerrorsarer eportedforeachedgeinTable 4.8.Theword-levelstatisticsfortheprimaryinputsarege neratedusingtheARMAmodel SIG1fromTable4.1. Finally,inordertodemonstratethecompatibilityofourap proachwithanexisting crosstalkminimizationtechnique,namely,busre-orderin g,were-orderthebuslinesby placingtwoofthelineswiththelowestcrosstalksusceptib ilitybetweenbuslineswiththe highestsusceptibility.Table4.9showsthedecreaseincro sstalkprobabilities,followingthe re-ordering.Table4.10givesthecrosstalkprobabilities obtainedforthebuslinesusing thenon-enumerativestatisticalestimationprocedurefor boththeoriginalaswellasthereorderedbus,comparedagainsttheprobabilitiesobtainedu singthestream-basedverication procedure.Theaverageestimationerrorisseentodecrease slightlyfrom3.7%forthe originalbus( =109 : 02 ; =83 : 2 ; =0 : 8)to2.9%forthere-orderedbus( =100 : 96 ; = 69 : 2 ; =0 : 4).Thisstudydemonstratesthattheproposedstatisticaln on-enumerative techniqueisreliable.4.4Conclusions Wepresentedanon-enumerativestatisticaltechniquetoev aluatebit-levelprobability ofcrosstalkeventswithinasystembusfromword-levelstat isticalparametersoftheinput 65

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Table4.8.Avg.crosstalkestimationerror-FIR Edge id Avg.err(%) Edge id Avg.err(%) x1 8.7 yout 15.6 x2 8.7 r0 8.7 x3 9.0 r1 11.4 x4 8.8 r2 15.5 x5 9.3 r3 11.6 x6 8.7 r4 21.0 x7 9.3 r5 9.2 x8 9.0 r6 30.4 x9 8.7 r7 12.0 x10 9.4 Table4.9.Crosstalkprobabilitiesonoriginalandre-orde redbuslinesanddecreasein crosstalksusceptibilityduetore-ordering Busline Original Re-ordered Decreaseincrosstalk(%) 1 0.30 0.20 +33.3 2 0.62 0.63 -1.6 3 0.64 0.61 +4.7 4 0.61 0.56 +8.2 5 0.61 0.64 -4.9 6 0.57 0.53 +7.0 7 0.54 0.56 -3.7 8 0.20 0.20 0.0 Table4.10.Estimationprobabilitiesfororiginalandre-o rderedbus Originalbus Re-orderedbus Busline Str.based NET Err(%) Str.based NET Err(%) 1 0.30 0.30 0.0 0.20 0.20 0.0 2 0.62 0.59 4.8 0.63 0.60 4.7 3 0.64 0.60 6.3 0.61 0.60 1.6 4 0.61 0.59 3.3 0.60 0.60 0.0 5 0.61 0.57 6.6 0.64 0.60 6.2 6 0.57 0.52 8.7 0.53 0.57 7.5 7 0.54 0.54 0.0 0.56 0.54 3.5 8 0.20 0.20 0.0 0.20 0.20 0.0 66

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data.Weintroducedasamplingtechniquetoquicklyevaluat edeniteintegralsofdiscrete randomvariablesduringtheestimationprocess.Thetechni quereducestheestimation complexityfromexponentialtolinearwithrespecttothebu s-width.Thetechniquehas beenecientlyappliedtoestimate intra-buscrosstalk .Thefollowingchapteraddresses the inter-bus crosstalkestimationproblematthelayoutlevelofdesigns .Thestatistical techniqueforintra-buscrosstalkestimationisintegrate dalongwitharoorplanneranda globalroutertopredictinter-buscrosstalkeects. 67

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CHAPTER5 FLOORPLAN-BASEDCROSSTALKESTIMATIONFORMACROCELL BASEDDESIGNS Inthischapter,weaddressthecriticalproblemofcrosstal kestimationbetweenthe dierentbusesatthelayoutlevelofadesign.Thisproblemi ssignicantinthatit's solutionprovidescrosstalksusceptibilityestimatesofv ictimwiresthatenabledesigners tooptimizeadesignforcrosstalk.Weproposeanestimation techniquetomeasurethe crosstalksusceptibilityofdierentnetsinthepostgloba lroutingphase,priortodetailed routingofdesigns.Globalroutingprovidestheapproximat eroutesofthewires.This isusedtocomputetheaggressorsofagivenvictimwirealong itsrouteanditscrosstalk susceptibilitywithrespecttothoseaggressors.Thecross talksusceptibilityofawireisgiven by:(1) P t ,theprobabilityofcrosstalkoccurrenceonthewireindie rentregionsalongits route;and(2) V peak ,theworstcasecrosstalknoiseamplitudeexperiencedbyth ewirealong itsroute. P t isestimatedusingaveryfastandaccuratestatisticalesti matorpreviously proposedbytheauthors. V peak isestimatedbypredictingthecross-couplingcapacitance s betweenneighboringwires,usingtheirglobalroutinginfo rmation.Placementandglobal routingaredoneusingCADENCESiliconEnsemble.Thepredic tedcrosstalkestimatesare comparedagainstthosebydetailedHSPICEsimulations.Ave rageerrorsarefoundtobe lessthan8%.5.1Thesignicanceoftheinter-buscrosstalkproblem Theinter-buscrosstalkestimationproblemisaprecursort ogeneratingcrosstalk-immune designs.Accurateestimationofthecrosstalksusceptibil ityofvictimnetsatthelayout-level allowsthedesignertorepeatthephysical-levelsynthesis stepswithcrosstalkminimization 68

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astheobjectivefunction.Thisprocessmaybeiterativeinn ature-startingwithaninitial layout,thedesignermayestimatethecrosstalksusceptibi lityofthevictimnetsandmay feedthisinformationbacktotheplacementorroutingphase softhesynthesisprocess.The routermaythenre-routethevictimswhicharemostsuscepti bleandgenerateanewlayout.Thecrosstalksusceptibilityofthevictimsinthenewl ayoutisthenreducedwithout violatingothertimingconstraints. Inthischapter,weproposeatechniquetoestimatetheinter -buscrosstalkwhichuses thestatisticalintra-buscrosstalkestimationprocessth atweproposedanddescribedin thelasttwochapters.Givenonlyword-levelstatisticsona bus,theintra-buscrosstalk estimatorcomputesabit-levelprobabilityforeachlineof thebus.Ourintra-buscrosstalk estimatorwasshowntohavegoodaccuracywithuptotwoorder sofmagnitudeinspeedup. Wechoosetoleverageonthisquickandaccuratetechniquewi thaviewtoestablishing thedependenceofcrosstalkatthelayout-level,ontheinpu tstatisticsonthevariouswires. Previously,thedependenceofdynamicpowerconsumptionon theinputstatisticstoa circuitwasestablishedin[77][78][79][80]. However,theintra-buscrosstalkestimationwasatthebeha vioral-levelofadesignand assumedallthelinesofabustobeplacednexttooneanotherf ortheentirelengthofthe bus.Thisassumption,whilereasonableforasystembusrunn ingfromaxedsourcetoa destination,maynotbetrueduringphysicalsynthesis.The routingistypicallyperformed wire-by-wireratherthanforindividualbuses.Thus,itisp ossibleforwireswithcommon sourcesanddestinationstodivergeatsomepointinthecirc uitandre-convergeatalater pointinthecircuit.Moreover,theinter-buscrosstalkest imationdemandsthatcertain physical-levelparametersofthedesignareaccuratelyacc ountedfor.Hence,weadopt anapproachwhichintegratesourintra-busestimatorwitht hephysical-levelinformation availabletousatthepost-globalroutingphaseofthedesig n. Therehavebeenpreviousattemptstosolvethecrosstalkest imationandreduction probleminthepost-globalroutingphaseofsynthesis[81][ 66][82][83].Thesetechniques aretargetedtowardsPCBsaswellasMulti-chipmodules(MCM s).Someoftherouting 69

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techniquesusedforcrosstalkminimizationarealsostrong enoughtohandleyieldimprovements,byminimizingthechancesofopencircuitsandshortc ircuits[84].However,these techniquesrelyonruntime-intensivegraphmanipulationt echniquesforcrosstalkestimation andarea-intensiveshieldingtechniquesforcrosstalkred uction.Whiletheseareconstructivetechniqueswhichtakeacrosstalkcostfunctionintoac countwhilesolvingtherouting problem,othertechniquessuchas[85][86]areiterativein nature.Delayaswellascrosstalk spikesareminimizedbyre-adjustingthespacebetweenthei nterconnectlinesofarouted design.Alternatively,successive ripupandrerouting ofindividualwiresleadstoincreasingly bettersolutions.Crosstalkinsideswitchboxesduringrou tinghasbeenstudiedin[87]and ILP-basedsolutionshavebeenproposedfortheirminimizat ion.Thesesolutions,although novel,areproposedatthephysical-levelofdesignabstrac tion.Theyneedprecisephysical levelinformationaboutthecircuitinordertorun.Ontheot herhand,ourapproachisto gatheronlyasmallfractionofthephysicallevelinformati onandpredicttherestsothat wecanleverageonthestatisticalestimationtechniquesth atwepreviouslyproposedforthe intra-buscrosstalkestimation.Thus,weareabletotakead vantageofthefastdesign-space explorationatthebehavioralandRT-levelswhileestimati ngeectsatthephysical-level. Inordertogeneralizeourtechniqueforacircuitlayout,in ourcurrentwork,weform compositebuses basedonglobalrouteinformationaboutneighboringwiresp rovidedbythe roorplanner.Besides,weextendtheapproachtousethesame physical-levelinformation tocomputeaworst-casecrosstalknoisepulseforeachwirei nthedesign. Theorganizationofthischapterisasfollows:Section5.2d escribesthefeaturesofthe placeandroutetoolusedinthiswork.Section5.3detailsho wwedecomposetheinter-bus crosstalkproblemsothatittransformstothemodelweusedf ortheintra-buscrosstalk problem.Section5.3,subsection5.3.1validatestheempir icalpredictionswemakeinthe post-globalroutingphaseofthedesignwithrespecttothep hysicalorderingsbetween victimwiresindierentroutingregionsatthelayoutlevel .Thisinformationiscriticalin estimatingthecross-couplingcapacitancebetweenthevic timwires.Section5.3,subsection 5.3.2alsodescribeshowweobtainthestatisticsontheaggr essorsofavictim.Section5.3, 70

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subsection5.3.3forms compositebuses togettheword-levelstatisticsalongalltherouting regionsofavictimwire.Section5.4detailstheanalytical evaluationofthetwocrosstalk susceptibilitymetricsnamely,thecrosstalkprobability onavictimwireanditsworst-case crosstalknoiseamplitudealongdierentregionsduringit sroute.Thissectionalsocombines theindividualcrosstalkprobabilityandworst-casenoise amplitudevaluesalongthevictim's routeintoasinglevalueforthecrosstalkprobabilityanda singlevalueforthecrosstalk noiseamplitudefortheentirevictimwire.Section5.5pres entsexperimentalresultsand theiranalysis.Finally,Section5.6drawsconclusions.5.2Theplaceandroutetool Toaccuratelypredictcrosstalkeectsbetweendierentwi resinthelayout,weutilize roorplaninformationaboutthedesign.Thisinformationis obtainedfromSiliconEnsemble, acommercialphysicalsynthesistoolfromCadence.Formacr ocell-baseddesigns,Silicon Ensemblesuperimposesa grid ontopofageneratedplacement.Eachcellinthegridis knownasa globalroutingcell (gcell).Everywirepassesthroughasequenceofgcellswhil e traversingfromthesourceterminaltothedestinationterm inal,asshowninFigure5.1. Separatemetallayersareusedforthehorizontalandvertic alrouteofeverywire.Thus, theapproximaterouteofanywireinthedesignisthesequenc eofgcellsthroughwhich itpasseseitherhorizontallyorvertically.Consequently ,thewireswhichpassthroughthe samegcellinthehorizontaldirectionareinthevicinityof oneanotherandareconsidered neighbors.Similarly,thewireswhichpassthroughthesame gcellintheverticaldirection arealsoneighborsofoneanother.Forexample,inFigure5.1 (b), WIRE1 and WIRE2 whichsharetwogcellsintheverticaldirection,areneighb orsinboththecells.Viasare usedatallintersectionstotransferfromthehorizontalla yertotheverticallayerandvice versa. Theglobalroutingphasedoesnotgivetheorderingofthewir eswithinagcell.It merelygivestheapproximaterouteofeachwire.Theorderin gofthewireswithinanygcell ispredictedusingtheplacementinformation.Forthehoriz ontaladjacency,itisassumed, 71

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gcell (a)Grid-basedrouting VIA WIRE 2 WIRE 1 (b)Neighboringwiresonthegrid Figure5.1.Globalroutingofwires basedonempiricalobservations,thatif module1 isplacedabove module2 ,thenawire originatingfrommodule1isalsoplacedaboveawireorigina tingfrommodule2.Forthe verticaladjacency,itissimilarlyassumedthatif module1 isplacedtotheleftof module2 thenawireoriginatingfrommodule1istotheleftofthewire originatingfrommodule2. Thus,afterplacementandglobalroutingphaseofthetoolwe obtainthefollowing information: Theapproximaterouteofeachnet. Theneighboringwiresinsideagcell. The ordering oftheneighborswithinthegcell. Havingobtainedtheabove,weformulatetheinter-wirecros stalkestimationproblem sothatitcanbeecientlyincorporatedintothepreviously proposedstatisticalestimation technique.Theprocedureissplitintoseveralsteps.Thero wisshowninFigure5.4.The dierentstepsareexplainedsubsequently. 72

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MODULE 2MODULE 1 (x2, y2) (x1, y1) wire 2 wire 1 wire 1wire 2 above y1 > y2 Figure5.2.Horizontalorderingofwiresduringglobalrout ingwire2 to the left of wire1 wire2 wire1 x1 < x2 MODULE 1 2 MODULE Figure5.3.Vericalorderingofwiresduringglobalrouting 73

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RTL NETLIST PEAK NOISE PULSE CROSSTALK PROBABILITYCOMPOSITE BUS MODELS FLOORPLAN TRACES PROFILE FLOORPLAN Figure5.4.Generalprocedurerow 5.3Modelingtheinter-wirecrosstalkproblem Thissectionexplainsindetailhowwemodeltheinter-wirec rosstalkestimationproblemsothatittsintotheintra-buscrosstalkestimationmo delthatwepreviouslyused. Modelingtheinter-wirecrosstalkestimationprobleminvo lvesthefollowingsteps: Establishingthewire-orderingassumptions. ProlingthedesignattheRT-levelsoastoobtainthebitval uesoneachwire. Formingthecompositebuseswithineachglobalroutingcell andestimatingthecouplingcapacitancesbetweenthewiresofeachbus. Thefollowingsubsectionsdescribeeachofthesestepsinde tail. 5.3.1Validatingtheempiricalwire-orderingassumptions Theglobalroute-levelassumptionsregardingtheexactwir eorderingatthedetailed routinglevelmaybeformallystatedasfollows: 74

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Table5.1.Wire-orderingvalidation Benchmark Horizontal Vertical DiEq 70.1% 66.8% FIR 74.3% 59.0% IIR 55.3% 71.0% FFT4pt 65.3% 69.2% DCT2pt 67.0% 71.1% If wire1 originatesfromamodulewhoseplacementcoordinatesare( x 1 ;y 1)and wire 2 originatesfromamodulewithplacementcoordinates( x 2 ;y 2),then y 1 >y 2= ) wire1 isplacedabove wire2 If wire1 originatesfromamodulewhoseplacementcoordinatesare( x 1 ;y 1)and wire 2 originatesfromamodulewithplacementcoordinates( x 2 ;y 2),then x 1
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C2C3CxxC Cx xCCxGNDGND GNDC1C2C3 R1R2R3GNDL LC1 CCC CCx xx xxGNDGNDGNDR2R3 R1 Figure5.5.Formationofthecompositebusfromglobalroute 5.3.3Compositebusformation Thenotionofdierentwiresactingasneighborsinsideaglo balroutingcellenablesus todenea compositebus foreverygcell.Formally,acompositebuswithinagcellisd ened asasetofwireswithsameordierentsourcesanddestinatio nswhichpassthroughthis gcellinthesamedirection(horizontalorvertical)alongt heirroute.Itisnecessaryforthe wirestopassthegcellinthesamedirection(horizontalorv ertical).Onlythenwillitbe ensuredthatthewiresarecoplanarandwillgiverisetocros stalkeects.Crosstalkeects betweenperpendicularwiresindierentmetallayersareco nsideredtobenegligibleinthis worksincetheoverlaplengthisverysmall. Eachgcellhasalistofdierentwirespassingthroughit.To gether,theyconstitutethe composite bus.Itshouldbenotedthatthecompletionoftheglobalrout ingphasedoes notxuptheexactcoordinatesofaroute.Hence,thewiresar estill rexible withrespect totheirpositions.Theirexactcoordinateswillbedetermi nedonlyafterdetailedrouting. 76

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Therefore,inthepostglobalroutingphase,weusea prediction methodtoestimatethe separationbetweenthewiresandthereby,thecross-coupli ngcapacitance C x .Thedetails ofthepredictionmethodareexplainedsubsequently. Figure5.5illustratestheformationofthecompositebus.T woglobalroutingcellsare shownalongwiththewirespassingthroughtheminthehorizo ntalandverticaldirections. Themagniedguresofthegcellsshowstherexible,coplana rwireswithcross-coupling capacitancesbetweenthemselves.Besides,eachwirehasan associatedwire-to-substrate capacitanceaswellasaresistance.Thus,thecompositebus isconvertedtothetraditional crosstalkmodelforbus-basedinterconnects.5.4Estimatingtheinter-wirecrosstalkmetrics Thissectiondescribestheestimationofcrosstalksuscept ibilityofeachnet.Thecrosstalk susceptibilitycomputationinvolves(i)crosstalkprobab ilityestimationforeachwireand (ii)themaximumcrosstalknoisepulseamplitudeestimatio nforeachwire.Thefollowing subsectionsdescribetheestimationofeachoftheseparame tersindetail. 5.4.1Crosstalkprobabilityestimation TheRT-Levelprolinggivesusthedatavaluesonallthewire softheRTLdesign.Since theplacementphaseinvolvesthecellsconstitutingtheRTL datapathandcontrollerwhile theglobalroutingphaseinvolvesthewiresintheRTLinterc onnect,thedatavalueson thewiresareknowninthepostplacementandglobalroutingp hase.Inotherwords,for agivengcell,thedatatransitionsoneverywireofacomposi tebusareknown.Hence,we areabletocomputethestatisticalparametersnamely,mean ,standarddeviation,andlag-1 temporalcorrelationforthecompositebus.Thestatistica lestimator,whichtakesthese parametersasinputs,quicklyevaluatesthecrosstalkprob abilityofeverywireintheglobal routingcellunderconsideration.Thestatisticalestimat orisrunonceforeverygcellalong awire'srouteandforallthewiresinthesynthesizeddesign 77

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d L wCx Figure5.6.Cross-couplinginparallelwires Foragivenwire,wearethusabletocomputeaseriesofcrosst alkprobabilities,correspondingtoeverygcellthroughwhichthewireisrouted.The seindividualprobabilitiesare comparedagainstdetailedHSPICEsimulationofRCmodelsco rrespondingtothosesame gcells.TheformationoftheRCmodelsisexplainedintheexp erimentalresultssection. 5.4.2Maximumnoisepulseestimation Themaximumnoisepulseonavictimwirewithinaglobalrouti ngcellisgivenin[16]. Fortheconvenienceofthereader,itisreproducedinEquati on5.1. V P = 1 1+ C 2 C X + R 1 R 2 (1+ C 1 C X ) (5.1) where C X isthecross-couplingcapacitancebetweentheaggressoran dvictimwires. C 1 and C 2 arethewire-to-groundcapacitanceswhile R 1 and R 2 arethelumpedresistancesof theaggressorandvictimwiresrespectively.Theparameter s C 1 C 2 R 1 ,and R 2 arexed foragiventargettechnology.Ontheotherhand,thecross-c ouplingcapacitance C X not onlydependsonthelengthofoverlapbetweentheaggressora ndvictimbutalsoontheir separation.Thus,thisparameterwillvaryfromgcelltogce ll. Theaggressorandvictimwiresobeytheequationforthepara llelplatecapacitorgiven below: C X = o A d = o L w d (5.2) 78

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where o and arethepermittivityofairandthedielectricconstantresp ectively, L is theoverlaplengthbetweenthewires, w isthewidthoftheoverlappingareasofthewires, and d istheseparationdistance,asshowninFigure5.6.Thus,for axedoverlappingarea anddielectric, C X / 1 d = ) C X;new C X;org = d org d new (5.3) Thedimensions L x L ofthegcellsareprovidedbythetechnologyleused.Ifther eare m wireswhichconstituteacompositebuswithinagcell,thent heinter-wireseparation d sep isestimatedas d sep = L m (5.4) Theoriginalinter-wireseparationdistance d org isassumedtobe0.6 mwhichisthe trackseparationinthelayouts.Theoriginalcross-coupli ngcapacitance C X;org iscomputed withthiswireseparationandEquation5.2.Thus,withineve rygcell,thecross-coupling capacitancebetweenthewiresofthecompositebusisgivenb y C X;gcell = C org d org d sep (5.5) = C org md org L (5.6) Oncethecross-couplingcapacitancesarecomputed,themax imumnoisepulseofavictim netwithinagcellisanalyticallyestimatedusingEquation 5.1.Theestimatednoisepulse iscomparedagainstthatfromthedetailedHSPICEsimulatio nofthecompositebuswires withinthegcell. 79

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5.4.3Modicationoftheestimationprocessusinguniformwiremodels-rms estimate Althoughtheabovetechniqueofcrosstalkprobabilityesti mationisaccuratewithrespect totheindividualglobalroutingcells,itstillsuersfrom thedrawbackofnotformulating asinglecrosstalkprobabilitymeasureandasingleamplitu deestimateforanentirevictim net.Thus,theeectofthesameneighborofavictimwhichact sasitsaggressorintwo dierentgcellswillbeevaluatedtwice,onceforeachgcell .Sincethereisacompleteoverlap inthecrosstalkeventswhichwilloccuronthevictimasares ultofthisaggressor,therewill bearedundancyintheestimationprocess.Inordertoallevi atethisdrawback,wepropose acostfunctionthatincorporatesthecrosstalkprobabilit yofavictimnetinsideeachglobal routingcellalongitsroutetocomputeasinglecrosstalkpr obabilityfortheentirevictim netwhichaccountsfortheeventoverlaps. Thecostfunctionusedisthe rootmeansquare (rms)valueofthecrosstalkprobabilities fromdierentgcellsalongavictimwire'sroute.Bydeniti on,thermsvalueofavarying quantityisastatisticalmeasureofitsmagnitude.Thus,on ceweobtainthecrosstalk probabilitywithineachgcellalongtherouteofaspeciedv ictimwire,theresultantcrosstalk probabilityofthewireisgivenby Pr wire = s p 2gcell n (5.7) where Pr wire istheresultantcrosstalkprobabilityoftheentirewire, p gcell istheprobabilityofthewirewithinthe i th gcell,andthereisatotalof n gcellsalongtheentire routeofthewire.WedemonstratethattheRMSvalueofcrosst alkprobabilitiestakesthe overlappingeventsfromthesameaggressorsindierentgce llsintoaccount. Lemma :Given k globalroutingcellsalongthepathofavictimwirewiththes ame aggressor,theoverlappingcrosstalkeventsonthevictimc anbecapturedusingtheroot meansquarevalueofthecrosstalkprobabilitiesineachoft he k gcells. 80

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Adjacency and ordering within each gcell and global routing after placement .DEF file Silicon Ensemble Verilog translator vhd2verilog VHDL Composite bus formation Macrocell library synthesis system High-level wire within each gcell Max noise pulse for each estimator Cross-coupling capacitance within each gcell for each wire Crosstalk probability Statistical intra-bus crosstalk estimator of composite bus Word-level statistics RT-Level Profiler Figure5.7.Experimentalrow Proof :Sincethereareanequalnumberofcrosstalkeventsineacho fthe k gcells,the crosstalkprobabilitiesinthesecellsareidentical.Lett hiscrosstalkprobabilitybe p gc Then,theRMSvaluefor k gcellsiscomputedas p rms = q p 2gc + p 2gc + p 2gc + :::ktimes k (5.8) = q k p 2gc k = q p 2gc = p gc Thisisthesamecrosstalkprobabilityasthatoftheoverlap pedcrosstalkevents.Moreover,0 p gc 1impliesthat0 p rms 1 81

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5.5Experimentalresults ThedetailedexperimentalrowisgiveninFigure5.7.Theout putofthehigh-level synthesissystemnamely,theRT-Levelnetlistofadesignis convertedfromstructuralVHDL toverilogandfedintoCadenceSiliconEnsemble.Theotheri nputtoSiliconEnsembleis thepre-characterizedmacrocelllibrary,speciedinthe LibraryExchangeFormat(.lef) SiliconEnsemblecompletesplacementandglobalroutingan doutputstheresultant designinthe DesignExchangeFormat(.def) .Thisoutputcanthenbedirectlyusedto determinetheroorplanninginformationsuchasapproximat ewireroutesandwireorderings, necessaryfortheformationofthecompositebuseswithinev erygcell.TheRT-levelnetlist isalsopassedthroughtheRT-levelprolerinordertogetth edatavaluesonallthewires. Oncetheprolingphaseiscomplete,we predict thecross-couplingcapacitancesbetween wiresineverygcell.Theaggressorandvictimresistancesa swellastheirwire-to-ground capacitancesarexedforagiventechnology.Inourcase, R 1 =23.8n, R 2 =21.6n, C 1 =0.4fF,and C 2 =0.2fF.Thedimensionsofeverygcellarealsodeterminedfr omthe technologyle.Inallourexperiments,eachgcellis18 m x18 m andthetargettechnology is0 : 35 .However,theproposedtechniqueisindependentofboththe gcelldimensionsas wellasthetargettechnology.Duetotheabsenceofexactcoo rdinatesofthewireroutes,the wireswithinagcellareassumedtooverlapfortheentirelen gthofthegcell.Experimental resultsshowthatthisisareasonableassumptioninthepost globalroutingphaseand underthisassumption,thepeakamplitudeestimatesmatcht hecorrespondingHSPICE simulationswell.5.5.1RCmodels Inordertoverifytheresults,weformRCmodelsforeverygce llthroughwhichagiven wirepasses.Sincewemodelcrosstalkasapattern-dependen tphenomenon,wesimulatethe modelwiththeproleddatastreaminHSPICEtocomputetheto talnumberofcrosstalk eventsthatoccuronthedierentwires.Thetotalnumberofc rosstalkeventsonawire dividedbythetotallengthofthesimulateddatastreamindi catesthecrosstalkprobability 82

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CCC C 12 R1 R2 R1 2 1 L1 Lm R1 x C x C L2L3 Figure5.8.TheRCmodelforeverygcell ofthewireintheparticulargcell.Fromthesimulationwave form,wecanalsomeasurethe peaknoiseamplitudeattainedbythiswireinthegcell.Thee stimationerrorsarecomputed bycomparingtheestimatedvaluesagainstthesimulationre sults.TheRCmodelsfollow theconventionalcrosstalkmodelforbus-basedinterconne cts,asshowninFigure5.8. InFigure5.8,thegcellhas m wires.Hence,theRCmodelhas m lines, L 1 to L m .The victimwire V isthethirdline L 3 intheRCmodel.Hence,thethirdwirehasanassociated lumpedresistance R 2andawire-to-groundcapacitance C 2.Theremainingwiresinthe RCmodelhavelumpedresistancesof R 1andwire-to-groundcapacitancesof C 1.The cross-couplingcapacitanceisequalto C X forallthewires. Table5.2givesthebenchmarkdetailswithrespecttothenum berofwirespresentin thesynthesizeddesigns.Thewiresoriginatefromnetsbelo ngingtofunctionalunits(FUs), registers(REG),multiplexers(MUX),andcontroller(CTRL ). Notethatthenumberofwires islessbecausethesenetsarebetweenmacrocells.Themacro cellsthemselvesareplacedand routedusingastandard-cellplaceandroutetool Table5.3showstheaccuracyofthestatisticalcrosstalkpr obabilityestimationmethod withinalltheglobalroutingcellsinthedierentdesigns. Theestimatesarecompared againstthetotalnumberofcrosstalkeventsobtainedfromt heHSPICEsimulationwaveform.Foraxedlengthofthevectorstimulusinthespicenet list,wecancomputethe correspondingcrosstalkprobability.Duetothelargenumb erofgcells,themaximumand 83

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Table5.2.Benchmarkdetails Benchmark Wires Totalwires FUs REG MUX CTRL DiEq 16 27 16 15 74 FIR 42 80 48 18 188 IIR 49 80 64 20 213 FFT4pt 45 48 48 16 157 DCT2pt 90 96 80 26 292 Table5.3.Crosstalkprobabilityestimationerrorscompar edtoHSPICE Benchmark Maxerror Minerror Avgerror Stddeviation DiEq 31.7% 0% 7.1% 8.4% FIR 33.3% 0% 1.4% 4.6% IIR 34.3% 0% 2.3% 7.8% minimumerrorsalongwiththethestandarddeviationofthee rrorsareprovided.Theminimumerroriszeroforallthedesignssincethecrosstalkpro babilityispreciselyestimated foramajorityofthewires.Thesourcesoferrorinthistechn iqueareasfollows: 1.Theempiricalassumptionsregardingthewireordering.A lthoughthesearefoundto betrueforamajorityofcases,theyarenottrueforallthegc ells. 2.Theestimationoftheinter-wirecouplingcapacitance.W eassumethatallthewires areequallyspacedinsideagcell.However,thismaynotbeth ecaseforallthegcells. 3.Theintra-buscrosstalkestimatorhassomeerrorbecause ofthesamplingprocedure. Thiserrorisrerectedintheinter-wirecrosstalkestimati ontoo. Eachvictimwirecanpassthroughglobalroutingcellswitho neormoreaggressors. Basedonthetotalnumberofaggressors,variousglobalrout ingcellsarecharacterized. Estimatesoftheworst-casenoiseamplitudeofavictimwire insidethedierentglobal routingcellmodelsarecomparedagainstthecorresponding HSPICEsimulation.Figure 5.10showsthesimulationofawirewhichpassesthroughagce llwithasingleaggressor. Thus,thereareonlytwowiresinthisgcell-thevictimwirea ndtheaggressorwire.The 84

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Table5.4.Executiontimesofcrosstalkprobabilityestima tion Benchmark StatisticalEstimation HSPICE DiEq 1.3min 2.6min FIR 4.3min 2.3hr IIR 95s 1.06hr Table5.5.Amplitudeestimatesagainstsimulatedvaluesfo rdierentgcells 2wires 3wires 4wires 5wires Est.(mV) Sim.(mV) Est.(mV) Sim.(mV) Est.(mV) Sim.(mV) Est.(mV) Sim.(mV) 20.5 20.0 30.1 25.0 39.4 42 48.2 45.0 estimatedmaximumamplitudeforthisglobalroutingcellmo delis20.5mV.Similarly,in Figure5.11,thevictimwiresharesagcellwiththreeotherw ires.Forthis4-wiregcell model,theestimatedmaximumamplitudeis39.4mV.Itistobe notedthattheamplitude forthesecondcaseishigherbecausetheinter-wireseparat ionforalargernumberofwires routedthroughthesameareaislessandconsequently,thecr oss-couplingcapacitanceis high.Theriseandfalltimesoftheinputsarexedat0.01psf orallexperiments.All experimentswereperformedona128MBSunUltra2dual-proce ssorworkstation. Forthecurrentmodelwherethestatisticalestimatorisrun onceforeachglobalroutingcellthroughwhichavictimwirepasses,theexecutionti mecomparisonsbetweenthe estimatorandHSPICEareprovidedinTable5.10.Thetotalex ecutiontimeforadesignis obtainedbymultiplyingthecrosstalkprobabilityestimat iontimeforagcellbytheproduct ofthetotalnumberofwiresinthedesignandtheaveragenumb erofgcellsthroughwhich eachwirepasses.ThusalthoughIIRhasalargernumberofwir esthanDiEq,itsexecution timeislowerbecausetheaveragenumberofgcellsthroughwh icheachwireinIIRpasses, ismuchlowerthanthatofDiEq. Table5.5comparestheanalyticallyestimatedworst-casec rosstalknoisepulseamplitudesagainstthesimulatedvaluesforglobalroutingcells withtwo,three,four,andve neighbors.Itmaybenotedthatincreasingnumberofneighbo rsleadstoincreasedcoupling capacitanceswhichinturn,leadstoincreaseinthepeaknoi seamplitude. 85

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Word-level statistics RT-Level Profiler Composite bus formation Adjacency and ordering within each gcell and global routing after placement .DEF file Silicon Ensemble Verilog translator vhd2verilog VHDL of composite busComparison HSPICE simulation validation HSPICE model forwire within each gcell Max noise pulse for each of crosstalk probabilities RMS value = of entire victim wire Crosstalk probability within each gcell for each wire Crosstalk probability Macrocell librarysynthesis system High-levelestimator Cross-coupling capacitance Statistical intra-bus crosstalk estimator Figure5.9.Experimentalrow(uniformwiremodel) 86

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Table5.6.Crosstalksusceptibilitydistributionofvicti mnets(0.00-0.40) Design 0.0-0.1 0.11-0.2 0.21-0.3 0.31-0.4 Stat HSP Stat HSP Stat HSP Stat HSP DiEq 10% 0% 0% 0% 20% 20% 40% 40% FIR 50% 40% 40% 40% 10% 20% 0% 0% IIR 30% 30% 40% 30% 10% 10% 0% 0% FFT4pt 10% 10% 40% 40% 10% 10% 30% 30% DCT2pt 60% 60% 20% 20% 0% 0% 20% 20% Table5.7.Crosstalksusceptibilitydistributionofvicti mnets(0.41-0.70) Design 0.41-0.5 0.51-0.6 0.61-0.7 Stat HSP Stat HSP Stat HSP DiEq 10% 10% 20% 30% 0% 0% FIR 0% 0% 0% 0% 0% 0% IIR 0% 0% 10% 10% 10% 10% FFT4pt 10% 10% 0% 0% 0% 0% DCT2pt 0% 0% 0% 0% 0% 0% Figure5.9showsthemodicationmadetotheexistingtechni quetoincorporatethe uniformwiremodel.Table5.8showstheaccuracyofthestati sticalcrosstalkprobability estimationmethodusingtheuniformwiremodel.Theresults arepresentedforthevictim wiresinthedierentdesigns.Theestimatesarecomparedag ainstthetotalnumberof crosstalkeventsobtainedfromtheHSPICEsimulationwavef orm.Givenaxedlengthof thevectorstimulusinthespicenetlist,wecomputethecorr espondingcrosstalkprobability. Duetothelargenumberofnetsforeachdesign,wegroupthemi nto3 errorbins ,depending ontheestimationerrorswithrespecttotheHSPICEsimulati ons.Forexample,intheFinite ImpulseResponselter,50%ofthevictimnetshavelessthan 10%estimationerror.Itmay beobservedthatforallthedesigns,80%ormoreofthevictim netshaveestimationerrors lessthan20%.Further,themaximumandminimumerrorsalong withtheaverageerrors areprovidedinTable5.9.Theminimumerroriszeroforallth edesignssincethecrosstalk probabilityispreciselyestimatedforamajorityofthewir es. 87

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Table5.8.ErrorbinsofestimationerrorswrtHSPICE(unifo rmwiremodels) Benchmark EstimationError 10% 10%-20% > 20% DiEq 60% 30% 10% FIR 50% 30% 20% IIR 50% 30% 20% FFT4pt 60% 20% 20% DCT2pt 70% 10% 20% Table5.9.EstimationerrorstatisticscomparedtoHSPICE( uniformwiremodels) Benchmark Maxerr Minerr Avgerr DiEq 66.7% 0% 14.2% FIR 33.3% 0% 10.0% IIR 30.0% 0% 11.0% FFT4pt 25.0% 0% 12.1% DCT2pt 25.0% 0% 8.1% Theexecutiontimecomparisonsbetweenthestatisticalest imatorandHSPICEare providedinTable5.10.Theanalyticalestimationprocessa chievesaspeedupofmorethan sixtimesoverthatofHSPICEsimulation.5.6Conclusions Wehavepresentedatechniquetoestimatethecrosstalksusc eptibilityofdierentnets inadesignduringphysical-levelsynthesis.Weusedtwomet ricsinordertomeasurethe crosstalksusceptibilityofeachwire.Therstwasacrosst alkprobabilityforthewirein Table5.10.Averageexecutiontimesofestimationcompared tosimulation(eachvictim wire) Benchmark StatisticalEstimation HSPICE DiEq 46s 7.0min FIR 41s 6.5min IIR 33s 6.3min FFT4pt 31s 6.8min DCT2pt 48s 7.1min 88

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Figure5.10.AmplitudesimulationinHSPICE-2-wiremodel 89

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Figure5.11.AmplitudesimulationinHSPICE-4-wiremodel 90

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dierentregionsalongitsroute.Thiswasevaluatedusinga fastandaccuratestatistical estimationprocedure.Thesecondwastheworstcasecrossta lknoisepulseamplitudeexperiencedbythewirealongitsroute.Foreachmetric,aseries ofvaluesobtainedforagiven wirealongitsrouteisthencombinedintoasinglevaluefort heentirewire.Comparisonof bothmetricsagainstdetailedHSPICEsimulationsshowgood accuracywithmuchshorter runtimes. 91

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CHAPTER6 BINDINGFORCROSSTALKMINIMIZATIONDURINGHIGHLEVEL SYNTHESIS Weutilizethecrosstalksusceptibilityinformationobtai nedforthevictimnetsofa designtodirectthehigh-levelsynthesisprocesstoproduc eanRT-leveldesignthatismore immunetocrosstalk.Thehigh-levelsynthesisprocesscons istsofthreemainstepsnamely, scheduling,allocation,andbinding.Initially,wecharac terizedierentdesignswithrespect tothecrosstalksusceptibilityoftheinputsandoutputsof theirfunctionalunits.Basedon thecharacterization,weformulateacostfunctiontoevalu atetheoverallqualityoftheRTlevelnetlistwithrespecttocrosstalk.Wethenmodifythet raditionalcliquepartitioning algorithmbyincorporatingthiscostfunctionintoit,soas togeneratecrosstalk-immune registerbindings.Comparisonswithregularregisterbind ingswhichdonotaccountfor crosstalk,showreasonablecrosstalkreduction.6.1The au tomatic d esign i nstantiation( audi )synthesissystem Beforemovingontothedetailsofthecrosstalkoptimizatio nalgorithm,itisnecessary todiscussthefoundationtoolusingwhichweperformhigh-l evelsynthesis(HLS).Thisis theAUtomaticDesignInstantiation(AUDI)systemdevelope dbyourresearchgroup. TheAUDIsystemwasdevelopedtoperformHLSonadesignspeci edintheformof adata-rowgraph.Thedatarowgraphiswritteninaspecicfo rmatknownasthe audi instantiationformat (.aif).The.aifleforasimpleexampleisshownbelow. Thelespeciestheprimaryinputsandoutputsofthedesign aswellastheintermediate edgesinthegraph.Boththe edge-id aswellasthe edge-width arespeciedforeachedge. Forexample,theinternaledge t 0hasawidthof8.Theinputsandoutputstothevarious 92

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operationsarespeciedintheorder leftinputid rightinputid ,and outputid fromleftto right.Forexample,operation1representsamultiplicatio n.Ithastwoinputs x 1and x 2 andoneoutput t 0. inputsx18x28x38x48x58x68x78x88outputsi8regst08t18t28t38t48t58op1MULT8x1x2t0op2MULT8x3x4t1op3MULT8x5x6t2op4MULT8t0t1t3op5MULT8t2x7t4op6SUB8t3x8t5op7SUB8t5t4iend AUDIthengoesthroughaninteractivesequenceofstepsandg eneratesstructuralVHDL implementationofthedatapath,controller,andtheoveral ldesign.Thestepsinvolvechoosingasuitableschedulingalgorithm,specifyingthenumber ofresourcestobeused,and choosingthetypeofbinding.Ifthenumberofresourcesisno tspecied,AUDIalwaysuses theminimumnumbernecessarytosatisfyagiventhroughput. Theinformationpertaining tothebindingofoperationstofunctionalunitsandedgesto registersisspeciedasaheader inthestructuralVHDLles.Theheaderinformationoftheda tapathlecorrespondingto the .aif leshownaboveisasfollows. --Filename:simple4_dp.vhd--Type:Datapath--Inputaiffilename:simple4.aif--CDFGstatistics:--*NumberofPI's:8 93

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--*NumberofPO's:1--*Numberofinternaledges:6--*NumberofOperations:7--*Conditionals:-12345--*Loops:-12345--*TypesofOperations:--DesignFlow/AlgorithmInformation:--*Scheduling:ASAP--*Allocation:Automatic--*Binding:Automatic--Interconnectstyle:Mulitplexor-based--DesignInformation:--Datapath:--*Registers:8--*Functionalunits:4--*NumberofMuxes:5--*NumberofBuses:0--*OperatorBindingInformation:--ResourceId=0type=MULT:--Index=0type=MULTwidth=8--MappedOps={op1op4}--Index=1type=MULTwidth=8--MappedOps={op2op5}--Index=2type=MULTwidth=8--MappedOps={op3}--ResourceId=1type=SUB:--Index=0type=SUBwidth=8--MappedOps={op6op7} 94

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--*RegisterOptimizationInformation:--Register#0(width=8,ctrl=-12345)=--{it5t3t0x1}--Register#1(width=8,ctrl=-12345)=--{t4t1x2}--Register#2(width=8,ctrl=-12345)=--{t2x3}--Register#3(width=8,ctrl=-12345)=--{x8}--Register#4(width=8,ctrl=-12345)=--{x7}--Register#5(width=8,ctrl=-12345)=--{x6}--Register#6(width=8,ctrl=-12345)=--{x5}--Register#7(width=8,ctrl=-12345)=--{x4}--Controller:--*Type:Moore--*Numberofstates:7--*Numberofcontrolbits:14-------------------------------------------------------------------Forexample,operations1and4whicharebothmultiplicatio ns,areboundtothesame multiplierinstance.Similarly,internaledges t 4, t 1,andprimaryinput x 2areboundtothe sameregisternamely,Register#1. Duringhigh-levelsynthesis,AUDIiscapableofperforming designoptimizationssuch asdynamicpoweroptimization[45]andleakagepoweroptimi zation[88][89][90][91].We introducecrosstalkoptimizationasanadditionalfeature intothesystem. 95

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6.2Crosstalkcharacterizationofdesigns UsingAUDI,wemakeapreliminarycharacterizationofdesig nswithrespecttocrosstalk intheirdatapaths.Thedatapathcrosstalkissub-dividedi ntothefollowingcategories: Crosstalkoftheregisteroutputs Crosstalkofthefunctionalunitoutputs Crosstalkofthemultiplexoroutputs Themetricusedformeasuringcrosstalkisthe crosstalkprobability betweenlinesofthe variousdatapathnets.Forexample,whilecomputingtheamo untofcrosstalkoftheregister outputs,wecomputethecrosstalksusceptibilityofeachli neattheoutputofeveryregister inthedesign.Ifthetotalnumberofregistersbeingusedis n reg andeachregisteris m -bits wide,wecomputeasetofcrosstalkcoecientscorrespondin gtothedierentbits.Foreach bit,thecrosstalkcoecientistheaveragecrosstalkactiv ityofthatparticularbitacross alltheregisters.Forexample,wecomputetheLeastSignic antBit(LSB)coecientas theaveragecrosstalkactivityontheLSBofalltheregister s.Similarly,wecomputethe crosstalkcoecientofeachoftheotherbits.Thisrational eforcomparingthesamebit acrossalltheregistersisderivedfromtheDual-Bitmodel[ 9]wheretheentirewordis groupedintodierentregionsbasedonbreakpoints.Bitsin thesameregionexperience similaractivity.Thus,alltheLSBsofthedierentregiste routputswillapproximately experiencethesameamountofcrosstalkactivityandtheira verageisagoodestimateof theactivity.Thus,for m -bitregisters,therewillbe m coecients.Ingeneral,thecrosstalk coecientcorrespondingtothe i thbiti.e. C i;reg ,isdenedasfollows: C i;reg = P n reg k =1 c i;k m (6.1) Similarly,wecomputetheamountofcrosstalkinthefunctio nalunitsandmultiplexors. Thecharacterizationismadeforthreedierentscheduling algorithms,whichareas follows: 96

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Table6.1.DetailsofDiEqdatapath Scheduling Registers FunctionalUnits Multiplexors ASAP 8 4 5 ALAP 8 3 7 FDS 8 3 7 Table6.2.DiEqdatapathcharacterization-asap Busline Registers FunctionalUnits Multiplexors 1 5% 6% 9% 2 6.9% 11.4% 14.2% 3 6.7% 12.3% 14.3% 4 6.1% 13.2% 13.7% 5 4.4% 12.1% 10.8% 6 2.8% 10.1% 7.8% 7 1.5% 7.1% 4.6% 8 1.0% 4.7% 3.2% TheunconstrainedAs-Soon-As-Possible(ASAP)algorithm Thelatency-constrainedAs-Late-As-Possible(ALAP)algo rithm thelatency-constrainedForce-DirectedSchedulingalgor ithm(FDS)whichminimizes resourceusage[92] Tables6.1-6.9reportthedatapathdetailsandthecharacte rizationresultsforthedifferentdesigns.Thecharacterizationentriesindicatethe averagecrosstalkactivityforeach edgeofthe8-bitresources.Forexample,inTable6.2,theLS Boftheregistershave5% crosstalkactivityontheaveragewhiletheMSBoftheregist ershave1%crosstalkactivity ontheaverage.6.3Bindingduringhigh-levelsynthesis Followingschedulingandallocationofresources,thelast stepinourhigh-levelsynthesis rowis binding .Thisconsistsofmappingdierentoperationsandedgesint hedatarow graphtotheavailableresourceinstances.Thebindingstep issubdividedintothefollowing: 97

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Table6.3.DiEqdatapathcharacterization-alap/fds Busline Registers FunctionalUnits Multiplexors 1 5.1% 10.5% 13.5% 2 7.1% 18.0% 20.8% 3 7.0% 18.9% 21.8% 4 6.2% 20.3% 21.0% 5 4.5% 19.1% 18.3% 6 3.2% 17.7% 14.5% 7 1.9% 10.9% 8.8% 8 1.3% 9.8% 6.5% Table6.4.DetailsofFIRdatapath Scheduling Registers FunctionalUnits Multiplexors ASAP 10 6 6 ALAP 10 3 6 FDS 10 3 6 Table6.5.FIRdatapathcharacterization-asap Busline Registers FunctionalUnits Multiplexors 1 4.9% 8.5% 11.6% 2 7.7% 13.8% 18.6% 3 7.1% 14.6% 19.0% 4 6.8% 14.9% 18.5% 5 4.7% 13.7% 16.6% 6 3.1% 10.9% 12.3% 7 1.3% 6.4% 6.1% 8 0.0% 3.6% 3.9% Table6.6.FIRdatapathcharacterization-alap/fds Busline Registers FunctionalUnits Multiplexors 1 4.9% 15.0% 14.3% 2 7.5% 23.3% 22.6% 3 6.8% 24.7% 22.1% 4 6.5% 25.6% 21.8% 5 4.0% 23.4% 17.9% 6 2.8% 20.9% 13.5% 7 1.3% 12.5% 7.1% 8 0.0% 6.6% 3.9% 98

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Table6.7.DetailsofIIRdatapath Scheduling Registers FunctionalUnits Multiplexors ASAP 10 7 8 ALAP 10 5 10 FDS 10 5 10 Table6.8.IIRdatapathcharacterization-asap Busline Registers FunctionalUnits Multiplexors 1 6.6% 7.0% 13.8% 2 11.1% 12.7% 23.7% 3 10.5% 12.7% 23.8% 4 11.3% 13.7% 26.1% 5 9.4% 13.9% 25.7% 6 9.5% 12.2% 23.5% 7 4.5% 9.5% 16.4% 8 2.3% 7.5% 9.5% Table6.9.IIRdatapathcharacterization-alap/fds Busline Registers FunctionalUnits Multiplexors 1 5.6% 11.4% 14.8% 2 9.3% 18.4% 24.3% 3 8.2% 18.0% 23.0% 4 8.2% 18.0% 23.5% 5 6.4% 17.1% 20.1% 6 5.9% 15.9% 19.3% 7 3.4% 9.7% 10.8% 8 1.9% 8.2% 8.5% 99

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Bindingofedgestoregisters. Bindingofoperationstofunctionalunitinstances. Thebindingofoperationstoaminimumnumberoffunctionalu nitsissimple.Basedon theschedulingalgorithmselected,theoperationsintheda ta-rowgraphhavedatadependenciesbetweenthem.Figure6.1showsanexampleoftwodie rentschedulesforthesame datarowgraph[93].Thus,intheASAPscheduleshown,operat ions3and7arescheduled inthesametimestep(tstep)andmaynotsharethesamemultip lierinstance.However,in theALAPschedule,theymaydososincetheyarescheduledind ierenttimesteps.Similarly,operations7and8whichmayshareamultiplierinstan ceintheASAPschedule,may notdosointheALAPschedule.TheASAPscheduleneedsaminim umoffourmultipliers andtwoALUswhiletheALAPscheduleneedsaminimumoftwomul tipliersandthree ALUs.Inordertominimizethenumberoffunctionalunitsuse d,thestrategyistokeep bindingdierentoperationstothesamefunctionalunitins tanceaslongasdatadependenciesarenotviolated.Thisisagreedyapproachandworkswel lforsmalltomedium-sized benchmarks. Thebindingofedgestoregistersishowever,moreinvolved. Itrstdeterminesthesetof compatible pairsofedges.Twoedgesaresaidtobecompatibleiftheyhav enon-overlapping lifetimesi.e.,iftheycanpotentiallysharearegister.Ba sedontheedgecompatibilities, a registercompatibilitygraph isformed.Theverticesrepresenttheedgesinthedatarow graphandtwoverticesareconnectediftheedgescorrespond ingtothosearecompatible [94][95][96]. Thenextstepinvolvesforming cliques intheregistercompatibilitygraph.Acliqueis denedasasubsetofverticesinthegraph,allofwhicharemu tuallyconnectedbyedges. Intheregistercompatibilitygraph,acliquewillbeformed byedgeswhicharemutually compatible. 100

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* * * +< * + +< + * 1 2 3 4 67 5 8 9 10 11 89 10 11 12 3 4 5 6 7 (b) ASAP (c) ALAP * * *+ +< 1 2 3 4 5 6 7 8 9 10 11 (a) Input DFG ASAP schedule ALAP scheduleFigure6.1.Asap/alapschedulesforadatarowgraph 101

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6.3.1Cliquepartitioning FindingthemaximalcliqueinagivengraphisaNP-hardprobl em.Amongtheheuristics proposedtosolveit,TsengandSieworek'sheuristic[97]ha sbeenthemostwidelyapplied tohigh-levelsynthesis.Thealgorithmisillustratedusin gFigure6.2. Startingwiththeinitialcompatibilitygraphhavingsixve rtices,therststepofthe Tseng-Sieworekalgorithmchoosesapairofverticeshaving thehighestnumberofcommon neighborsasseed.Thisisthepairofvertices v1,v3 whichhavetwocommonneighbors namely, v8 and v7 .Thus, v1,v3 ischosenastheseed.Vertices v1 and v3 arenowmerged intoacommonvertex.Ifavertexwaspreviouslyconnectedto both v1 and v3 ,asingle edgenowconnectsittothemergedvertex v1,v3 .Ifavertexwaspreviouslyconnected toeither v1 or v3 butnotboth,itisnolongerconnectedtothemergedvertex.T hus,in thenewgraphwithvevertices,edge v1,v6 isremovedbecausetherewasnoconnection from v3 to v6 intheinitialgraph.Thenextstepofthealgorithmselectsv ertex v7 since itisconnectedtovertex v1,v3 .Thesubsetofvertices v1,v3,v7 isthenidentiedasa clique.Thealgorithmthensearchesforanewvertexpairast heseedforthenextclique. Wheneverthereismorethanoneoption,thealgorithmselect sonerandomly.Supposeit picksthepair v6,v8 asthenextseed.Inthenextstep, v2 isaddedtoformthesecond clique v6,v8,v2 [94]. Whileapplyingthisalgorithmtodeterminetheedgeswhichm aysharearegisterinthe datapath(withoutcrosstalkconsiderations),thecurrent cliquepicksacompatiblevertex whichsharesthemaximumnumberofneighborswithit.Ifther eismorethanonepossibility, thevertexwhoseselectionwould excludetheminimumnumber ofneighborsoftheclique, isselected.Thisistoensuremaximalityoftheclique. Similarly,whilebindingforcrosstalkminimization,thec urrentcliquealwayspicksa compatiblevertexsharingthemaximumnumberofverticeswi thit.However,tobreak atiebetweentwoormorevertices,itinterleavesthedatast reamsoftheverticeswhich arepartofthecurrentcliqueandeachoftheverticeswhicha recandidatesforselection inthecurrentiteration.Thecrosstalkactivityforeachse lectionisthencomputed.The 102

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6 8 7 1 2 8,6 1,3 2 6 8 3 {v1, v3, v7}{v2, v6, v8} {v1, v3, v7}{v1, v3, v7} 262 8 7 Figure6.2.Cliquepartitioningexample vertexwhichresultsinthelowestcrosstalkactivityforth enewclique,isnallyselected. Figure6.3illustratestheprocedure. Inthegure, v1,v3 arepartofthecurrentclique.Thealgorithmcurrentlyhasa choice ofthreeverticesnamely, v2 v5 ,and v7 forexpandingtheclique.Theusualprocedureis tochooseonevertexrandomly.However,forminimizingcros stalk,weinterleavethedata streamofthecurrentcliquewitheachcandidatevertexandc omputethecrosstalkactivity, asshowninthegure.Thevertexcorrespondingtothelowest crosstalkactivityischosen. Suppose Y isthelowestvalue.Then,wechoose v5 asthecandidatevertexandupdatethe clique.6.4Experimentalrowandresults TheexperimentalrowisshowninFigure6.4.Eachdesignisin puttotheAUDIsystem inthe audiintermediateformat (.aif)format.Ofseveralpossibleschedulingalgorithms availableinAUDI,werestrictourchoicestotheASAP,ALAP, andFDSschedulingalgo103

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1, 3 27 5 {x21, x22, x23...}{x51, x52, x53...}{x71, x72, x73...} {x11, x31, x12, x32, x13, x33, ....} {x11,x31,x21,x12,x32,x22,...}{x11,x31,x51,x12,x32,x52,...} {x11,x31,x71,x12,x32,x72,...} register crosstalk = Xregister crosstalk = Yregister crosstalk = Z Compare and choose minimum Figure6.3.Cliquepartitioningforcrosstalkminimizatio n rithmssinceourmainobjectiveistoexplorethebindingspa ceforcrosstalkminimization. Schedulingisfollowedbyresourceallocationandthenbybi nding.Bindingmaybeperformedinthe regular mannerwithouttakingcrosstalkactivityintoaccount.Ont heother hand,wecanprogramthesystemtoperform crosstalk-aware bindingwhichminimizes crosstalkactivityintheregisters.Forthesameschedulin galgorithm,thegeneratedRTL datapathsaredierentfordierentbindings.Eachdatapat hisproledwithdatastreams fromdierentdataenvironmentsusingtheRT-Levelproler thatwepreviouslydeveloped. TheRTLdesignsarethensimulatedusingCadencenclaunchan dthecrosstalkactivityat theoutputsofthedierentregistersiscomputedandcompar ed. Tables6.10-6.12comparetheregularandthecrosstalk-awa rebindingsofdierent designsintermsoftheregistercrosstalkactivity.Thesch edulingalgorithmchosenforboth bindingsisthesamesothatweareabletocaptureonlytheee ctofthecrosstalk-aware bindingontheregistercrosstalkactivity.Thescheduling algorithmchosenforeachdesign 104

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ASAPALAPFDS Resource allocation Regular Crosstalk-aware binding profiler RTL Statisticalcrosstalk estimator RTL design 1RTL design 2 binding Compare AUDI Input: .aif format Figure6.4.Experimentalrowforrtlcrosstalkoptimizatio n 105

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Table6.10.Crosstalkreductionduetocrosstalk-awarebin ding(asapscheduling)-DiEq RegisterID Crosstalkreduction(%) 1 2.0% 2 0.0% 3 0.0% 4 0.0% 6 0.0% 7 1.0% 8 12.0% Table6.11.Crosstalkreductionduetocrosstalk-awarebin ding(asapscheduling)-FIRlter RegisterID Crosstalkreduction(%) 1 4.1% 2 12.2% 3 6.3% 4 16.4% 5 0.0% 6 -1.7% 7 7.2% 8 7.9% 9 0.0% 10 0.0% istheonewhichgivesthelowestcrosstalkactivitywiththe regularbinding.Weobtain thisinformationfromtheinitialcharacterizationofthed esign.Thus,wecomparethe proposedcrosstalk-awarebindingtechniqueagainstthere gularbindingfortheminimum crosstalk-activityschedule. FromTables6.2and6.3,itcanbeseenthatthecrosstalkacti vityinthedatapath fortheDiEqexampleislesserincaseoftheASAPschedule.H ence,inTable6.10,we testtheeectivenessofthecrosstalk-awarebindingagain sttheregularbindingforthe ASAPschedule.SincetheDiEqexamplehaseightprimaryinp uts,AUDIusesonlyeight registers,whichistheminimumnumberrequiredforafeasib ledesign.Thepercentage reductionincrosstalkduetothedierenceintheregularan dcrosstalk-awarebindingsis reportedregisterbyregisterforeachdesign.Similarly,i nTables6.11and6.12,wechoose 106

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Table6.12.Crosstalkreductionduetocrosstalk-awarebin ding(alapscheduling)-IIRlter RegisterID Crosstalkreduction(%) 1 2.0% 2 4.5% 3 5.1% 4 4.2% 5 0.0% 6 1.5% 7 2.0% 8 9.0% 9 2.0% 10 3.4% Table6.13.Comparionofruntimes Design Schedule Regularbinding Crosstalk-awarebinding DiEq ASAP 3s 59s FIR ASAP 2s 59s IIR ALAP 2s 57s theschedulewhichisthelowestintermsofcrosstalkactivi tyforeachdesignandtestthe proposedcrosstalk-awarebindingagainsttheregularbind ingforthechosenschedule. Table6.13comparestheruntimesfortheentirehigh-levels ynthesisprocessforthe regularandcrosstalk-awarebindingchoices.Thecrosstal k-awarebindingtakesmoretime becauseoftheinterleavingofdatastreamsandcomputingth ecrosstalkactivitywhile choosingacandidatevertexforexpandingtheclique.Table s6.14comparetheresource usageforacommonscheduleandbothtypesofbinding,foreac hdesign. Table6.14.Comparionofresourceusage Regularbinding Crosstalk-awarebinding Design Schedule Reg FU Mux Reg FU Mux DiEq ASAP 8 4 5 8 4 6 FIR ASAP 10 6 6 10 6 6 IIR ALAP 10 5 10 10 5 12 107

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6.5Conclusions Wehavepresentedacrosstalk-awareregisterbindingtechn iqueduringhigh-levelsynthesisthatminimizedcrosstalkactivityattheregisterou tputsintheRT-leveldesign.We initiallycharacterizedthedesignswithrespecttothreed ierentschedulingalgorithms.Usingtheschedulewhichfavorslowercrosstalkactivity,wec omparedtheproposedcrosstalkawarebindingwiththeregularcliquepartitioning-basedb inding.Reductionsinregister crosstalkactivityofover16%wereobtainedovervariousde signs.Integrationoftheproposedbindingalgorithmwithaconstructivecrosstalk-awa reschedulinghasthepotential tominimizethecrosstalkactivityattheoutputsofallthed atapathunitsandispartofthe futurework. 108

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CHAPTER7 CONCLUSIONSANDFUTUREWORK ThecurrenttrendsinVLSIresultinnewandcomplexproblems withrespecttocircuit design.Miniaturizationofdevicesforportabilityandthe continuingeectsofMoore'slaw createuniqueinteractionsbetweenthedevicecomponentsw hichaecttheoverallperformanceandreliability.Crosstalkisonesuchphenomenoncau sedbytheproximityofthe interconnectwires.Unwantedinteractionsbetweenthesew iresaectboththereliability andperformanceofthecircuitadversely.Thus,itbecomesi mperativeforthedesignerto accuratelyestimateandoptimizecrosstalkinordertogene rateerror-freedesigns. Duetotheadvantageoffastdesignspaceexplorationattheh igherlevelsofdesignabstractionandtheprovenspeedandaccuracyofstatisticalm odelsinparticular,thisdissertationproposedfastandaccuratestatisticalestimatorso fcrosstalktoestimatethecrosstalk susceptibilityofthelinesofbus-basedinterconnects.Th eestimatortookonlytheword-level statisticsofthedataonthebusasitsinputandcomputedbit -levelcrosstalkprobabilities foreachline.ComparisonswithdetailedHSPICEsimulation sindicatedspeedupsof10x ormorewhilemaintainingreasonableaccuracy.Thestatist icalestimatorwasfurthermodiedtolinearizeitscomplexitywithrespecttothebus-wid thandenhanceitsscalability. Themodiedestimatorresultedinspeedupsofovertwoorder sofmagnitudecomparedto HSPICE.Thedrawbackinthistechniqueisitstradeobetwee nspeedandaccuracy.The techniquecanbemademoreaccuratebutatthecostofincreas edruntimes.Thenumber ofsamplesspeciedbytheuserduringthetrapezoidalinteg rationis,infact,oneofthe sourcesoferrorinthetechnique.Moreover,thistechnique consideredidealbusgeometries. Withtheintra-buscrosstalkestimatorinplace,wethenuse dittodeterminethe crosstalksusceptibilityofdierentbusesatthelayoutle velofdesignabstraction.This 109

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wasamorechallengingproblem,consideringthefactthatwe neededaccuratephysicallevelinformationontheinterconnectlineswhichwasnotav ailabletousatthehigh-level. Toovercomethis,weusedtheCadenceSiliconEnsemblePlace andRoutetooltoperform placementandglobalroutingonthedesigns.Besides,weuse dtheCadenceNCLaunchtool toperformRT-Levelprolingonthedesignsandobtainthewo rd-levelvaluesonthewires inthelayout.Therouteofavictimwirewasthensplitupinto acollectionofglobalrouting cells(gcells)andthepreviouslydevelopedintra-busesti matorwasrunoneachgcell.We alsousedanalyticalequationstocomputetheworst-casecr osstalknoisepulseonthevictim linewithineachgcell.Subsequently,theindividualgcell valueswerecombinedtoforma singlevaluefortheprobabilityofcrosstalkonavictimlin easwellastheworst-casenoise amplitudeonit,duringitsroute.Thesourcesoferrorinthi stechniquearethedierences inourpredictedestimatesofthephysical-levelparameter ssuchascouplingcapacitanceand wireroute,andtheactualvaluesoftheseparameterswhicha reafunctionoftheplaceand routetool.Withmoreinformationfromthecircuitlayout-l evel,thetechniquecanbemade moreaccurate. Finally,weusedthecrosstalkprobabilitymetrictominimi zecrosstalkactivityatthe registeroutputsofadesignduringhigh-levelsynthesis(H LS).Initially,wecharacterized thecrosstalkactivityindesignswithrespecttodierents chedulingalgorithms.Foragiven schedule,wethensearchedthebindingspaceduringtheHLSp rocesstondasuitablebindingwhichminimizedcrosstalkattheoutputoftheregisters .Inordertodothis,wemodied thetraditionalclique-partitioningalgorithmtoselectn odeswithminimumcrosstalkactivity duringeachiterationofthealgorithm.Themaindrawbackof thistechniqueisits locality i.e.itisagreedyheuristicwhichexploresthebindingspac ealone.Exploringtheentire high-levelsynthesisspacecanresultinbettersolutionsf ordecreasingthecrosstalkactivity intheentiredatapath. Theresearchdoneinthisworkfortacklingthecrosstalkest imationandoptimization problemleavesroomforfuturework.Someofthemarelistedb elow. 110

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Duringtheintra-buscrosstalkestimation,weassumethata llthewiresinabusare equallyspacedandrunparallelfortheentirelengthoftheb us.However,sucha perfectgeometrymaynotberealizedallthetime.Hence,the statisticalestimation algorithmmayneedtobemodiedtoaccountforirregulariti esinthebusstructure. Whileestimatingthecrosstalkeectsonvictimnetsatthel ayout-level,anintrinsic assumptionmadebyuswastheavailabilityofthevaluesonal ltheaggressorwires insideagivenroutingchannel.Thisassumptionmayneedtob emodiedinviewof thefactthateachcircuithassometimingassociatedwithit .Thus,ifagivenvictim hastwoadjacentaggressorsoneithersideofit,itmaybepos siblethatonlyoneof themhasavaluewhiletheotheronemaybeinthehigh-impedan cestate.Itmay alsobepossiblethatalltheaggressorshavevaluesonthema tsomeinstant.Thus, specic timingwindows mayneedtobeassociatedwitheachroutingchannel. Sincethestepsofscheduling,allocation,andbindingduri nghigh-levelsynthesisare inter-dependent,solvingonlyoneofthemforcrosstalkmay resultinasub-optimal solutionattimes.Thus,ifthecrosstalk-awarebindingalg orithmproposedbyusis integratedwithcrosstalk-awarescheduling,thecrosstal kactivityattheoutputsof thefunctionalunitsandmultiplexorscanbesignicantlyr educedaswell. 111

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ABOUTTHEAUTHOR SuvodeepGuptareceivedtheBachelorofEngineering(B.E.) degreeinElectronicsand CommunicationEngineeringfromBirlaInstituteofTechnol ogy,Mesra,Indiain1999.He thenjoinedthegraduateprograminthedepartmentofComput erScienceandEngineering attheUniversityofSouthFlorida,Tampa,USA.Heobtainedh isMastersdegreeinComputerScienceandEngineeringin2002andcontinuedforaPhD .Duringthecourseofhis graduatestudies,hepublishedmultiplejournalandconfer encepapers.Besidesresearch,he alsotaughtseveralcoursesattheundergraduatelevelinth euniversity.Heistherecipient oftheACM-SIGDAscholarshipforgraduatestudents.Hisres earchinterestsincludedesign automation,high-levelsynthesis,low-powerVLSIdesign, andphysical-levelsynthesis.He isamemberofACMandIEEE.