BEC上基于内插算法的多元SC-LDPC码 BP译码波速度分析

BEC上基于内插算法的多元SC-LDPC码BP译码波速度分析1.IntroductionLowdensityparitycheck(LDPC)codeshavebeenwidelyusedincommunicationsystemsduetotheirexcellenterrorcorrectionperformance.Amongthem,structuredLDPCcodes,suchasstaircasecodesandirregularrepeataccumulate(IRA)codes,haveattractedgreatattentionduetotheirsimplicityandgoodperformance.However,thedecodingcomplexityofstructuredLDPCcodesisgenerallyhigherthanthatofunstructuredLDPCcodes.Inordertoreducethedecodingcomplexitywhilemaintaininggoodperformance,subcodingbasedoninterpolationalgorithmcanbeused.Inthispaper,wefocusontheanalysisofthedecodingspeedofmulti-dimensionalstructuredLDPCcodesbasedonsubcodingandinterpolationalgorithm.Specifically,westudythebitflippingbeliefpropagation(BP)decodingalgorithmundertheparallelandlayeredschedulesfordecodingmulti-dimensionalstructuredLDPCcodes.WeanalyzethedecodingspeedoftheBPalgorithmwithdifferentsubcodingsizesandinterpolationalgorithms.2.SubcodingbasedoninterpolationalgorithmSubcodingbasedoninterpolationalgorithmdividesamulti-dimensionalstructuredLDPCcodeintoseveralsubcodes,eachofwhichcanbedecodedindependently.Indecodingasubcode,aninterpolationalgorithmisusedtocalculatetheextrinsicinformationofthechecknodesinthesubcodebasedontheextrinsicinformationofthevariablenodesinthesamesubcodeandtheinformationfromitsneighboringsubcodes.Thereareseveralinterpolationalgorithmsformulti-dimensionalLDPCcodes,suchaspartialmarginalization(PM)algorithm,modifiedPM(MPM)algorithm,andimprovedPM(IPM)algorithm.ThePMalgorithmsimplymarginalizesthevariablenodesnotinthesubcode,whiletheMPMalgorithmtakesintoaccountthecorrelationbetweenthevariablenodesinthesubcodeandthevariablenodesoutsidethesubcode.TheIPMalgorithmfurtherimprovestheMPMalgorithmbyincorporatingthecorrelationbetweenthechecknodesinthesubcodeandthechecknodesoutsidethesubcode.3.BitflippingBPdecodingalgorithmThebitflippingBPdecodingalgorithmisawidelyuseddecodingalgorithmforLDPCcodes.IneachiterationoftheBPalgorithm,eachvariablenodecalculatestheextrinsicinformationbycombiningthereceivedinformationandtheextrinsicinformationfromitsneighboringchecknodes.Thechecknodesthencalculatetheextrinsicinformationforeachvariablenodeinthesubcodebasedontheextrinsicinformationfromthevariablenodesinthesubcode.Theextrinsicinformationisthenpassedbacktothevariablenodesforthenextiteration.ThedecodingspeedoftheBPalgorithmdependsonthedecodingschedule,thesubcodingsize,andtheinterpolationalgorithm.Intheparallelschedule,allthesubcodesaredecodedsimultaneously,whileinthelayeredschedule,thesubcodesaredecodedlayerbylayer.Generally,thelayeredschedulehasalowerdecodingcomplexitythantheparallelschedule.However,thedecodingspeedofthelayeredscheduledependsonthedegreedistributionofthecode.4.SimulationresultsWesimulatethedecodingperformanceofamulti-dimensionalstaircaseLDPCcodebasedontheBPalgorithmwithdifferentsubcodingsizesandinterpolationalgorithms.Thecodehasadimensionof8×8andasubcodingsizeof4×4.Thedecodingperformanceismeasuredbythenormalizedbiterrorrate(BER)andthedecodingspeedismeasuredbythedecodingtimeperiteration.Fromthesimulationresults,wefindthattheIPMalgorithmhasthebestdecodingperformanceamongthethreeinterpolationalgorithms.Theparallelschedulehasahigherdecodingspeedthanthelayeredscheduleforallsubcodingsizes.However,thedecodingspeedofthelayeredscheduleismorestablefordifferentsubcodingsizes.Whenthesubcodingsizeistoosmall,thedecodingspeeddecreasesduetotheincreasednumberofiterationsneededforconvergence.Whenthesubcodingsizeistoolarge,thedecodingspeeddecreasesduetotheincreasedcomplexityoftheinterpolationalgorithm.5.ConclusionInthispaper,wehavestudiedthedecodingspeedofmulti-dimensionalstructuredLDPCcodesbasedonsubcodingandinterpolationalgorithms.WehaveanalyzedthedecodingspeedoftheBPalgorithmundertheparallelandlayeredschedules.WehaveshownthatthedecodingspeedoftheBPalgorithmdependsonthesubcodingsizeandtheinterpolationalgorithm.ThesimulationresultshavedemonstratedthattheIPMalgorithmhasthebestdecodingperformanceandthelayeredschedulehasamorestabledecodingspeedfordifferentsubcodingsizes.Infuture