Density Evolution for Nonbinary LDPC Codes Under.pdf

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1、IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.55,NO.3,MARCH2009997DensityEvolutionforNonbinaryLDPCCodesUnderGaussianApproximationGeLi,IvanJ.Fair,Member,IEEE,andWitoldA.Krzymien´,SeniorMember,IEEEAbstract—Thispaperextendstheworkondensityevolutioncodeensemblespecifiedbya

2、degreedistributionpair.Withtheforbinarylow-densityparity-check(LDPC)codeswithGaussiansymmetryofthechannelanddecodingalgorithmasoneofitsapproximationtoLDPCcodesoverGF.Wefirstgeneralizethefundamentalassumptions,thismethodcanbeappliedtoawidedefinitionofchannelsymm

3、etryfornonbinaryinputstoincludeclassofbinary-inputsymmetric-outputchannels,including-aryphase-shiftkeying(PSK)modulatedchannelsforprimeandbinary-modulatedchannelsforthatisapowerof.Forthebinaryerasurechannel(BEC),binarysymmetricchannelthewell-defined-ary-inpu

4、tsymmetric-outputchannel,weprove(BSC),andadditivewhiteGaussiannoise(AWGN)channel,asthatundertheGaussianassumption,thedensitydistributionforwellastovariousiterativedecodingalgorithmsthatfallintothemessagesundergoingdecodingisfullycharacterizedby0categoryofmes

5、sagepassingalgorithms.Thedensityinvolvedquantities.Assuminguniformedgeweights,wefurthershowthatinthisnumericaltechniqueistheprobabilitydensityfunctionthedensityofmessagescomputedbythechecknodedecoder(CND)isfullydefinedbyasinglenumber.Wethenpresentthe(pdf)ofthemes

6、sagespassedateachdecodingiteration.UnderapproximatedensityevolutionforregularandirregularLDPCatree-likeassumption,densityevolutioncomputestheexactcodes,andshowthatthe0-dimensionalintegrationinvolveddensityofmessagesastheyevolvefromiterationtoiteration,canbes

7、implifiedusingadimensionalityreductionalgorithmforandcanbeusedtoevaluatetheasymptoticbit-errorprobabilitytheimportantcaseof.Throughapplicationofapproximateofthecodeensembleforeachiteration.Allowingforinfinitedensityevolutionandlinearprogramming,weoptimizethede

8、greedistributionofLDPCcodesoverGFandGF.Theoptimizediterations,itcanbeusedtodeterminethedecodingthreshold,irregularLDPCcodesdemonstrateperformanceclosetothewhich