LDPC编译码方法综述

Vol.17No.3118SPACECRAFTENGINEERING17320085LDPC(,100094)LDPC,,LDPC,,LDPCLDPC:TN911.22:A:167328748(2008)0320118205EncodingandDecodingAlgorithmsofLDPCCodesGuoYongfu,ZhouAosong(BeijingInstituteofSpacecraftSystemEngineering,Beijing100094,China)Abstract:Withitsbestperformanceandsimpledecoderstructure,LDPCcodeswillbewidelyusedindeepspaceexploration,satellitecommunicationsandotherfields.Whilebrieflyintrodu2cingLDPCcodesareintroducedbriefly,thispapersummarizestheencodinganddecodingalgo2rithms.Theencodingalgorithmisdescribedintwosteps:theconstructionofparity2checkmatrixandtheencodingmethodbasedonparity2checkmatrix.Astodecodingalgorithm,MPdecodingmethod,BPdecodingmethod,Min2Sumdecodingmethod,Bit2FlippingmethodandWeightedBit2Flippingmethodarediscussed.Thedevelopmentofencodinganddecodingmethodsisana2lyzedaswell.Keywords:spacecraft;LDPCcodes;encoding;decoding;parity2checkmatrix:2007210231;:2008201213::(1982-),,,:LDPC1,,,,Shannon,RS,TurboLDPC,ShannonLDPC,,,,LDPC,(VeryLargeScaleIntegration,VLSI)[1][2]LDPC(ETSI)DVB2S2LDPCNASACCSDSCCSDS131.12O22(EX2PERIMENTALSPECIFICATION),LDPC[3],,,,,,,,LDPC2LDPCLDPC(LowDensityParity2Checkcodes,)Gallager60[4],,,,,LDPC1996,MacKayLDPCTurbo,LDPC[5],LDPCShannonBIAWGN,1/2LDPC,Shannon0.0045dB[6]LDPC(VariableNodes)(CheckNodes)(Edges),;,;,,,,,LDPC3LDPCLDPC,,3.1LDPC:,,,GallagerPEG;,,,,3.1.1GallagerGallager(n,j,k)LDPCH[4](n,jk):j,1,k1;,,H,,,,,,,,3.1.222,[7]LDPCGallager,,,1,,3.1.3PEGHuXiao2YuPEG(ProgressiveEdge2Growth)[8-9]i1,,,i,PEG,,PEGGallager,9113:LDPC3.1.4(Quasi-Cyclic)LDPC[10]Pilli,,PHmlnl,:H=P11P12P1(n-1)P1nP21P22P2(n-1)P2nPm1Pm2Pm(n-1)Pmnij:{0,1,,l-1,}LDPC1,,1/lLDPC,,CCSDS131.12O22(EX2PERIMENTALSPECIFICATION)LDPCLD2PC,3.2,LDPC,,;HG,G,O(n2),,,,3.2.1LUmnH=[AB],Amk,Bmm,k+m=nBLU,LU,,,LULUnLU,Su2ChangChae[11]PABR(PivotingandBit2ReversingAlgorithm),B,LUPABRH4,LU,LULDPC,LU,2.2.2ThomasJ.Richardson[12]LDPCH1,H,,1Fig.1Structureofapproximatelylowertriangularparity-checkmatrix1,,O(n+b2),b,(1)b,,b,,3.2.3IRA[7][13]HB(B2.2.1),(IrregularRepeatAccumulate,IRA),,,BLUb=0,IRA,,B,LDPC,DVB2S2LDPC0.1dB[14]3.3LDPC,02117,,,,,;LDPC,,LDPC,,,,LDPC,LDPC,LD2PC,,LDPC,,,4LDPC4.1(MessagePassing,MP),,,,,LDPC,,,,,4.2,,,,(BeliefPropagation,BP),,,BP,,,,,,BP,LDPCBP,,BP,,4.3(Min2Sum)BP,,,4.4(Bit2Flipping,BF),01,,,,,,,BP,4.5KouYu(WeightedBit2Flipping,WBF)[15],,,,,,4.6,LDPC,,,,,,1213:LDPCBP,,BPBP,,BP,,,BER,,LD2PC,5LDPC,,,LDPC,,,,BERLDPC,,,,LDPC,,DVB2S2CCSDS131.12022IEEE802.11LDPC,LDPC(References)[1].LDPC[J].,2002,(9):15219[2],,.LDPC[J].,2007,3[3]CCSDS131.12022.Lowdensityparitycheckcodesforuseinnear2Earthanddeepspaceapplications[S].CCS2DS,2007[4]GallagerRG.Lowdensityparitycheckcodes[J].IRETransactionsonInformationTheory,1962,8(3):2082220[5]MacKayDJC.NealRM.NearShannonlimitper2formanceoflowdensityparitycheckcodes[J].Elec2tronicLetters,1996,32(18):164521646[6]Sae2YongChung,DavidForneyG,ThomasJRichard2son.Onthedesignoflow2densityparity2checkcodeswithin0.0045dBoftheShannonlimit[J].IEEECom2municationLetters,2001,5(2)[7]RichEchard,Shih2ChunChang.The2rotationlow2densityparitycheckcodes[J].Globecom,2001[8]HuXiao2Yu,EleftheriouEvangelos,ArnorldDieter2Mi2chael.Progressiveedge2growthTannergraphs[J].In:ProceedingsofGlobecom2001,SanAntonio,2001[9]HuXiao2Yu,EvangelosEletheriou,AmoldDM.Regu2larandirregularprogressiveedge2growthTannergraph[J].IEEETranssctionsonInformationTheory,2005,51(1)[10]SehoMyung,KyeongcheolYang,JaeyoelKim.Quasi2cyclicLDPCcodesforfastencoding[J].IEEETrans2actionsonInformationThoery,2005,51(8)[11]Su2ChangChae,Yun2OkPark.Lowcomplexityenco2dingofregularlowdensityparitycheckcodes[C].Ve2hicularTechnologyConference,2003.VTC20032Fall.2003IEEE58thVolume3,Issue,October629,2003[12]ThomasJRichardson,RdigerLUrbanke.Efficientencodingoflow2densityparity2checkcodes[J].IEEETransactionsonInformationThoery,2001,47(2)[13]ETSITR102376V1.1.1.DigitalVideoBroadcasting(DVB)userguidelinesforthesecondgenerationsys2temforbroadcasting,interactiveservices,newsgath2eringandotherbroadbandsatelliteapplications(DVB2S2)[S].EBI,2005[14]MustafaEroz,SunFengwen,LinNanLee.DVBS2lowdensityparitycheckcodeswithnearShannonlimitperformance[J].InternationalJournalSatelliteCom2municationNetwork,2004,22:2692279[15]KouY,LinS,FossorierM.Lowdensityparitycheckcodesbasedonfinitegeometries:arediscoveryandnewresults[J].IEEETransactionsInformationTheory,2001,47(10):271122736(:)22117