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1、392IEEECOMMUNICATIONSLETTERS,VOL.12,NO.5,MAY2008GeneralizedCombiningMethodforDesignofQuasi-CyclicLDPCCodesYuanhuaLiu,XinmeiWang,RuweiChen,andYuchengHeAbstract—AgeneralizationoftheChineseRemainderTheo-analyzedinSectionIII.SimulationresultsofseveralQC-rem(CRT)combiningmethodisp
2、roposedtodesignmuchmoreLDPCcodesdesignedbytheCRTcombiningmethodandandbetterquasi-cyclic(QC)LDPCcodeswhentheparitycheckthegeneralizedcombiningmethodarecomparedinSectionmatricesofthecomponentcodesaregiven.ItcandesignaIV.Finally,SectionVconcludesthepaper.muchlargerclassofQC-LDPC
3、codeswithsimilarperformancebylooseningtheconditionfordeterminingtheintermediateparameters.Bypermutingtheblockrowsoftheparitycheckmatricesofthecomponentcodes,alotofQC-LDPCcodeswithII.Preliminariesmuchless6-cyclesandbetterperformancecanbedesigned.AtaBERof10−6someQC-LDPCcodesdes
4、ignedbytheTheparitycheckmatrixHofaQC-LDPCcodebasedongeneralizedcombiningmethodoutperformthosedesignedbytheL×LcirculantpermutationmatricescanberepresentedasCRTcombiningmethodby0.5dB.⎡⎤IndexTerms—Low-densityparity-checkcodes,quasi-cyclic,⎢⎢⎢⎢Ia11Ia12...Ia1n⎥⎥⎥⎥circulantpermutat
5、ionmatrix.⎢⎢⎢⎢Ia21Ia22...Ia2n⎥⎥⎥⎥H=⎢⎢⎢⎢........⎥⎥⎥⎥,(1)⎢⎢⎢⎣....⎥⎥⎥⎦I.IntroductionIam1Iam2...IamnOW-densityparity-check(LDPC)codes,firstproposedLintheearly1960s[1]andre-discoveredin1996[2],whereaij∈{0,1,...,L−1,∞}andIaij(1≤i≤m,1≤j≤n)haverecentlyattractedmuchattentionduetotheirc
6、apacity-representsanL×Lcirculantpermutationmatrixobtainedbyapproachingperformanceandlowdecodingcomplexity.AsancyclicallyshiftingtherowsoftheidentitymatrixItotherightattractiveclassofLDPCcodes,quasi-cyclic(QC)LDPCcodesbyaijtimes.ThezeromatrixofsizeL×LisdenotedbyI∞.arewellsuita
7、bleforcertainpracticalapplicationssincethey⎡⎤⎢⎢a11a12...a1n⎥⎥caneasilybeencodedusingsimpleshift-registerswithlinear⎢⎢⎥⎥complexity[3].Inaddition,well-designedQC-LDPCcodesof⎢⎢⎢⎢a21a22...a2n⎥⎥⎥⎥S(H)=⎢⎢⎢⎢........⎥⎥⎥⎥(2)moderatelengthcanperformaswellasrandomLDPCcodes.⎢⎢⎢⎣....⎥⎥⎥⎦A
8、ChineseRemainderTheorem(CRT)combiningmethodam1am2...amnwasproposedin
