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DEv_LDPC.pdf

DEv_LDPC

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2011-12-24 0人阅读 举报 0 0 暂无简介

简介:本文档为《DEv_LDPCpdf》,可适用于工程科技领域

IntroductionHighspeedandhighqualityarealwaysdemandedofcommunicationssystemsAsoneoftheapproachesforachievingtheserequirements,thedevelopmentoferrorcorrectingcodesthatcorrectmoreerrorsisattractingattentionLowdensityparitycheckcodes(LDPCcodes)areknownaspowerfulcodesthatareabletoperformclosetotheShannonlimitThereforeseveralstandardshavedecidedtoadoptLDPCcodes,andimplementationistakingplacegraduallyAtthesametime,inthedatastoragefield,theadventofhighdefinitiondisplaysandhighdefinitiontelevisionbroadcastinghasstimulatedtechnologicaldevelopmentssuchasBlurayDiscdiscsandholographicmemoriesthatcanrecordlargevolumesofdataHighdensityrecordingtechniquesareessentialtoachievingalargestoragecapacityThedata(strengthofmagneticfieldorreflectedlight)whichisreadfromtherecordingmediaisweaker,andsolikelytobemoresusceptibletoerrorsConsequently,inordertoachievehighdensityrecordingthatmaintainsthesamedataquality,stillstrongererrorcorrectingcodesareneededThissituationissimilartothatinacommunicationsystem,inwhichincreasesinspeedmustmaintainthesamecommunicationqualityLDPCcodesareanareaofactiveresearchinadvancedcommunicationsystems,advanceddatastoragesystems,andsimilarsystems(),()Incidentally,anothererrorcorrectingcodehasbeendiscoveredinrecentyearstheturbocodesdevelopedbyCBerrouetalinFranceinTurbocodesareknowntobeabletoperformclosetotheShannonlimitBothTurboandLDPCcodesareattractingattentionasthenextgenerationoferrorcorrectingcodesTurbocodesarecodesdevelopedfromconvolutionalcodes,andthealgorithmderivedfromtheViterbidecodingalgorithmisprimarilyusedasthedecodingmethodOntheotherhand,LDPCcodesaredescendedfromtheblockcodesinventedbyRGGallagerinthesThatis,thesecodeshaveadifferenthistoricalbackgroundandbelongtoadifferentcodesystem,buthavetheexistinghighesterrorcorrectingcapabilitiesinthattheyperformclosetotheShannonlimitTheswereaperiodwhenmechanicalrelaysandvacuumtubeswerestillinuseforcomputerpartsThisiswhenthehistoryoferrorcorrectionstartedAtthattime,RWHammingbecamefrustratedwiththetimewastedoncomputerproblemsatBellLabs,ashehadtorestarthisprogramfromscratchaftercarryingoutnumericalcalculationsoverseveralweeksHethendevelopedasetofcodesthefamousHammingcodeswhichareatechniqueforidentifyingtheerrorlocationsandrestoringthecorrectdataCurrenterrorcorrectingcodeshavetheiroriginintheHammingcodesAsGallagerpredictedthatagreaternumberoferrorswouldhavetobecorrectedinthefuture,theinventionofLDPCcodeswasanapproachtoachieveaperformanceclosetotheShannonlimitbysimpleiterativecalculationsonthereceiversideThistechniquerequiredsequentialcircuitsusingmemorycellsHowever,accordingtothedemandsofthetimes,itwasdesirablethatthedecodersbeconfiguredbycombinationallogiccircuitswithouttheuseofmemorycellsasaresult,LDPCcodeswereforgottenInthepresentday,withthefundamentaltechnologiesestablishedandduetotheurgentdemandsofthemarket,LDPCcodes,whichhavebeenforgottenfornearlyyears,arebeingrediscoveredTheappealofLDPCcodeswhichareageold,yetatthesametimenewcannowbeseenFiguresummarizestherecentresearchtrendsinLDPCcodesThetypeofparitycheckmatrixintheLDPCcodeisshownatthecenterofthefigureontheright,codedesignandanalysistechnologyontheleft,decodingmethodsanddevicestoimplementtheminthelowerbox,applicationsintheupperbox,contendingtechnologiesandothersOncheckingresearchtrendsagainstthehistoryofLDPCcodes,itisunderstoodthatitwasimportantformanufacturerstoaccumulateknowhowwhileevaluatingthefeasibilitybasedonthemanufacturingtechniquesshownontheleftofthefigureAdditionally,inanticipationoffuturetechnologicalgrowth,theauthorspressedforwardwithdevelopment,notinawaythatfocusesmoreenergyondevelopmentofLDPCcodesthatareexcessivelyrestrainedbyexistingtechnologies,butinsteadinamannerthatimplementsversatileLDPC·DevelopmentofLowDensityParityCheckCodesINFORMATIONCOMMUNICATIONSLowdensityparitycheck(LDPC)codes,whichareamongthemostpowerfulerrorcorrectingcodes,canachieveperformanceclosetotheShannonlimitItisdifficulttoevaluatetheperformanceofLDPCcodesbysoftwaresimulationonly,becauseittakesmuchtimeandlaborTosolvethisproblem,theauthorshavedevelopedtheenvironmentfordesigningandevaluatingLDPCcodesonhardwareForimplementationofLDPCdecoderintohardware,theauthorshaveworkedoutnewcomputationmethods–theapproximationtotheloglikelihoodratioandtheminimumsearchmethodbasedonthedistributioncountsorting,andevaluatedtheirperformancebythisenvironmentThispaperdescribesthedetailsandresultofthemeasurementperformedusingthedevelopedexperimentalsystemDevelopmentofLowDensityParityCheckCodesTakashiMAEHATAandMasahikoONISHIcodesthatencompassthosetechnologiesThispaperreportsonthedevelopmentenvironmentandelementaltechnologies(approximationtotheloglikelihoodratio()andminimumsearchmethod())fortheLDPCdecoderdeveloped,andtheexperimentalapparatusdesignedfortheirapplicationThisapparatussupportsmultilevelmodulation(QAMtoQAM)techniques,whichareusedforwiredandwirelesssystems,aswellasOFDMmodulationsystemsDesignEnvironmentThedesigncycleshowninFigwasimplementedindevelopingtheLDPCencoder,decoder,OFDMtransmitterandreceiver(amongothers)whichareusedfortheexperimentalapparatusAsthefirststep,thecodedesign,includingtheparitycheckmatricesandgeneratormatricesandalgorithmdesignarecarriedout,andtheyareinputintoconfigurationandcircuitdesignasthesecondstepHere,theauthorsdevelopedthemodelgeneratorthatdealswithallorpartofthecircuitdesignautomaticallySo,insecondstepthegeneratorcandesignanencoderandadecoderautomaticallyafterenteringparameterstooptimizethedesignTobemorespecific,arangeofparameterscanbeinput,asshowninFig,toachieveatradeoffbetweenthecircuitscaleandtheprocessingspeedandautomaticallydesignmodelsthatcanprocessfromseveralMbstoseveralGbsSEITECHNICALREVIEW·NUMBER·OCTOBER·NumericalcalculationDesigningofcodesandalgorithmsConfigurationCircuitdesignVerificationModelgeneratorAccelerationHardwareIntheLoopFigConceptualdrawingofdesigncycleFigModelgeneratorwindowDataEntryibitibitobitTxDEn:OneShotORORSyncRstPnEnSPEndatadin:CntlPsSLoadPSEnSyncRstEncOut:EncOutEndout:dout:dout:dout:ParaEncOutEnsloadupdownmodq(:)enarstMakeParytyStartEncLoadEncCntlEnOutEnORTxDatao:NewEncobitNewEncEnLDPCEncoderFigLDPCencodertestbenchTransmissionpathmodelAWGN,fadingFPGAdownloadLDPCdecoderFigSystemsimulationandaccelerationenvironmentforsimulationApplicationMarginalperformanceMarginalperformanceImplementationAnalysisRandomcodeEncoderLDGMTurbocodeDecoderMethodforgeneratingparitycheckmatrixRegularNonregularRegularityRandom×Quantumcryptography,security,sensornetworkDatacompressionDelayedsignalHighordermodulationCommunicationcapacityanalysisDeviceDecodingprocessingtechniquesTannergraphBayesiannetworkBP,DE,GA,EXITGraphtheoryErrorfloorWaterfallGirthPerformanceanalysisApplicationStorageGBaseT,Opticalcommunication(av)DVBS,WiMAX,UWB,()Pictureimage(Erasure)SumProductUMPBP,UMPAPPλMIN,AMinOffsetBPBasedASICFPGADSP(firmware)FigResearchtrendsinLDPCcodesFigureshowstheperformanceverificationtestbenchforanLDPCencodergeneratedbythismodelgenerator,whichenablescomparisonbetweenthecodewordencodedbythenumericalcalculationandtheoneencodedwithHDLUtilizingthemodelingblocksshowninFig,itispossibletoestimatetheperformanceatthetopsystemlevelunderachannelclosetoanactualchannelwithcomplicatedfrequencycharacteristicsThisleadstoashorteneddevelopmentperiodwhenthespecificationsforanewsystemarebeingformulatedFurthermore,thismodelisequippedwithahardwareinterface,andincaseswherethecomputationloadishighandseveralnumericalcalculationsarenecessaryoveralongperiodoftime,apartofcomputationcanbeswitchedtoandoperatedonhardwareThisenablesanadequateandhighlyaccuratethoughtexperimenttobeperformedinashortperiodoftimeInaddition,allthefunctionscanbeswitchedtohardwareprocessingandthebiterrorratecanbecheckedusingbitsButinthiscase,thesystemrequiresanactualchannel,sothatuncontrollabledisturbancessuchasclockjitterspecifictoactualmachines,analogwaveformdistortion,powersupplynoise,andotherfactorsgetmixedinHence,byrepeatingthesebasicinvestigationsstepbystep,theperformancelimitscanbeascertainedInthefollowingsections,theauthorsreportonanapproximationtotheloglikelihoodratioandtheminimumsearchmethod,bothofwhichhaveagreatimpactonthedesignofahighspeeddecoderSystemOverviewOverallconfigurationThissectiondescribestheconfigurationoftheexperimentalapparatusdevelopedrecentlyFigureshowsaschematicdiagramofthetransmittingsystem,withitsbasicspecificationslistedinTableTransmissionsignalsareinputtoadatamodulatorviatheLDPCencoderTheyareGraycodedandmultilevelmodulatedforeachsubcarrierthereAfterinverseFouriertransformation,thesignalsareoutputtothechannelThereceivedsignalsfromthechannelareFouriertransformedandequalizedbyanadaptivefilterwhichisestimatedfromachannelThentheyareinputtotheLDPCdecoder,whichcomprisesahorizontalstepandaverticalstep,viatheloglikelihoodratiocomputationTheloglikelihoodratioisusedasaninitialvaluefortheiterativealgorithmintheLDPCdecoder,whichcorrectserrorsbyupdatingthe“aposterioriprobabilityratio,”andoutputtheresultsasthereceiveddataFigureshowsanexampleofanequalizedQAMconstellationTheconstellationinFig(a)isobservedwithoutAWGN,andinFig(b)isobservedwithAWGNinthechannelApproximationtologlikelihoodratioFigureshowsthatnoiseaffectstheconstellationsUsingthisconstellationblurring,thereliabilityvaluesofalldatareceivedarecomputedastheloglikelihoodratioEquation()isthedefinitionoftheloglikelihoodratioforQAM:where,uiandvidenotethecoordinatesoftheconstellationwhichbelongstoagroupinwhichtheithbitis‘’and‘’,respectivelyxisthecoordinateoftheequalizedconstellationEquation()isnotsuitedforhighspeedsignalprocessingbecauseitincludescomplexarithmeticoperationslikeexponentialandlogarithmicfunctionsandtheircomputationloadisproportionaltoamultiplicityofmodulationIntheexperimentalapparatusdevelopedrecently,·DevelopmentofLowDensityParityCheckCodesTableBasicspecificationsofexperimentalapparatusADGIremovalFFTTransmissionpathequalizationLoglikelihoodratiocomputingunitLDPCencodingDatamodulationIFFTGIinsertionDATransmitteddataLinemanipulationunit(horizontalstep)Stringmanipulationunit(verticalstep)LDPCdecodingunitReceiveddataChannelFigConfigurationofexperimentalapparatuspointsNumberofFFTpointsGuardintervalpointspointsDatamodulationQPSKQAM,QAMQAMChannelencodingdecodingLDPCcode(R=)FUMPAPPdecodingParitycheckmatrixRegularGallagerCodesN=,K=,J=cyclesfreeFigReceivedconstellation(a)Freeofnoise(b)WithnoisetheauthorsdevelopedanewapproximationtotheloglikelihoodratioTheauthorsfocusedontheoutputoftheloglikelihoodratiowhichwasconnectedtothesubsequentLDPCdecoder,andderivedthiscomputingmethodfromalinearapproximationtoEquation()()FigureoutlinestheoperationoftheUMPdecodingmethod()usedintherowoperation(horizontalstep)Itindicatesthattheα(truevalue)obtainedafterthiscomputationcanapproximatethefirstminimumabsolutevalueofx,andEquation()expressesthisprocessFurthermore,theauthorshaveanewinterpretationofthisoperationIncomputingthetruevalue,thesmallertheabsolutevalueofβis,themoreitaffectsthecalculationresultTheauthorsnoticedthattherowoperationworksasakindoffilterwhichisweightedtodecreasetheeffectsofthesecondorthirdminimumvaluesEvenifaroughapproximationisusedtothelargeabsolutevalue,theapproximationerrorisalleviatedbythefilterfunctionoftherowoperationunit(horizontalstep)Figures(a)and(b)showthedecodingcharacteristicswithanapproximationtotheloglikelihoodratioandtheUMPdecodingmethod,andshowthattheerrorcorrectioncapabilityofUMPnearlycoincideswiththatofUMPwithproposedLLRSpecifically,thearithmeticvolumeusingtheconventionalmethodincreasedexponentiallywithmultilevelmodulation,butthenewmethodalleviatedthevolumeasalinearincreaseItcanbeseenfromTableandFigthatthearithmeticvolumeisgreatlyalleviatedascomparedtotheconventionalmethodMinimumvaluesearchAsshowninFig,thesimplifiedLDPCdecodingalgorithmrequiressearchingtheminimumvalueintheSEITECHNICALREVIEW·NUMBER·OCTOBER·f(x)∑f(xi)x()()()()()xminαmnxminxminFigOutlineofrowoperationunit(horizontalstep)ModulatedmultilevelnumberConventionalmethodApproximationtologlikelihoodratio●�Arithmeticvolume●�●�●�●�●�●�FigComparisonofarithmeticvolumeTableComparisonofarithmeticvolumeConventionalmethodApproximationtologlikelihoodratio(Approximationmethodconventionalmethod)ModulatedmultilevelnumberQAMCNRdBBERQAM,length=,rate=BitErrorRateUMPUMPwithProposedLLR●�●�●�●�●�●�Fig(b)QAMbiterrorCNRdBBERQAM,length=,rate=BitErrorRateUMPUMPwithProposedLLR●�●�●�●�●�Fig(a)QAMbiterrorrowoperationunit(horizontalstep)ThissearchtimeisimportanttoachievehighspeeddecodingPreviously,atournamentformula,suchastheoneinFig,hasbeenusedforsearchingitButwithatournamentformula,theoutputsofthemagnitudecomparatorsinagivenstepbecometheinputsofthemagnitudecomparatorsinthenextstep,andsoitwaitsforthejudgmentoutputandthenadvancestothenextstepTherefore,itwasthoughtthattherewouldbealimitonhowsignificantlyprocessingdelaycouldbeimprovedNow,theauthorssucceededinreducingprocessingdelaybycreatinganewminimumvaluesearchmethodbasedonthedistributioncountingsortwiththeexperimentalapparatusdevelopedinourlaboratoryAnexplanationondistributioncountingsortisgivenfirstThisisakindofsortingalgorithm,whichfindsthefrequencydistributionfromtheentereddataandthendecidestherankingofdataonthebasisofcumulativedistributionasshowninFigWhatmakesthisalgorithmremarkableisthatthelistofascendingordercanbeobtainedwithoutamagnitudecomparisonbetweenelementsHere,tointroduceintotheexperimentalapparatus,theauthorsappliedthissortingalgorithmtotheminimumvaluesearchmethodMoreoverthesearchmethodsuitableforahighspeedsignalprocessingwasalsodevelopedFigureshowsanovelminimumvaluesearchmethodthatsolvesthisissuebyutilizingthenatureofthedistributioncountingsortInthisformula,thenumericalvalueisfirsttransformedintoaformwhichexpressesthelengthbyacontinuous,andtheminimumvalueisthendetectedbybitlogicalproductInaddition,byinversetransformation,theminimumvalueisfinallyobtainedInFig,itisassumedthatthetransformfunctionisg(x)=xtosimplifydiscussionHowever,insuchacase,whenintegrationisconducted,thereoccurstheproblemthatmanywiringresourcesarerequiredaftertheconversionConsequently,thetransformfunctionghadtobeselectedtoreducethewiringresourcesThistime,consideringtheimplementationoftheconversionandreverseconversioncircuitandthecharacteristicsoftheUMPdecodingmethoddescribedinFig,theauthorschoseatransformfunctionwhichtransformsfinelyinthecaseofasmallinputandcoarselyinthecaseofalargeinputTableshowsthistransformfunction,andthecircuitsinFigaretheconverterandreverseconverterIntherowoperationunit(horizontalstep),computationisperformedbytheapproximationminimumvaluederivedfromthistransformfunctionFigureshowstherelationshipbetweentherowweightandprocessingdelayThemaximumprocessingdelaybythedistributioncountsortingisnomorethan·DevelopmentofLowDensityParityCheckCodesxxxxk······ValueOrder➀Creation➁Search➁OrderFrequencyValue|x|FigDistributioncountsorting|x|Value➀Transformxxxky=g(|x|)➁Bitlogicalproductg(x)=xstmin······FigMinimumsearchmethodbydistributioncountsortingFirststepSecondstepMinimumvalueFourthstepThirdstepSmallyzvzyyysxsssssxxxxxxxsFigTournamentsystemTableTransformtable|x|g(x)=log(x)InternalexpressionnsecandscarcelychangeswithanincreaseintherowweightOntheotherhand,thetournamentselectionmethodshowsamonotonouslyincreasingtendencyConsequentlyinrowweight,therowoperationunit(horizontalstep)usingdistributioncountsortingoperatesaboutfourtimesfasterthanwhenusingthetournamentmethodExperimentalResultsTheauthorsevaluatedtheerrorcorrectioncapabilitiesofLDPCcodesusingtheabovementionedtechniquesThedatamodulationofallsubcarrierswassetatfromQPSKtoQAM,andmeasurementswerecarriedoutInFig,theresultsofnumericalcomputationswithfixedpointsimulationareshownforcomparisonThecomparisonresultsindicatethatnosignificantdegradationisgeneratedbetweenthetwoandthecorrectioncapabilitycurvesestimatedbynumericalcomputationscanbeobtainedasexpectedTheresultsindi

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