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1、ISIT 2006, Seattle, USA, July 9 14, 2006ACombiningMethodofStructuredLDPCCodesfromAffinePermutationMatricesSehoMyungandKyeongcheolYangDongSeekParkDept.ofElectronicsandElectricalEngineeringAdvancedResearchLab.PohangUniversityofScienceandTechnology(POSTECH)GlobalStandardsandResearchTeamPohang,Ky
2、ungbuk790-784,KoreaSamsungElectronicsCo.,LTD,KoreaEmail:{bighead,kcyang}@postech.ac.krEmail:dspark@samsung.comAbstract—Inthispaperwepresentaclassofstructuredbyafactor1/L,whenL×Lcirculantpermutationmatriceslow-densityparity-check(LDPC)codesfromaffinepermutationareemployed.Itisalsoeasiertocontro
3、ltheircyclepropertiesmatrices,calledtheAPM-LDPCcodes,whichareageneralizationintheirconstructionprocess,ascomparedwithrandomLDPCofquasi-cyclicLDPCcodes.Wegiveanecessaryandsufficientcodes.conditionunderwhichanAPM-LDPCcodehasacycleandintroduceasimplemethodtoconstructAPM-LDPCcodesofThemaincontribu
4、tionsofthepaperareasfollows.First,largelengthbycombiningthoseofsmalllengthbasedonthewepresentaclassofstructuredLDPCcodesfromaffineChineseRemainderTheorem.Inparticular,weshowthatthepermutationmatrices,calledtheAPM-LDPCcodes.TheyaregirthofAPM-LDPCcodesobtainedinthismethodisalwaysageneralizationo
5、fQC-LDPCcodesandaredifferentfromlargerthanorequaltothoseofgivenAPM-LDPCcodes.theLDPCcodesstudiedbyO’SullivanandSmarandache[12].WeshowanecessaryandsufficientconditionunderI.INTRODUCTIONwhichanAPM-LDPCcodehasacycleandintroduceaLow-densityparity-check(LDPC)codes,firstdiscov-simplemethodtoconstruct
6、APM-LDPCcodesoflargelengtheredbyGallager[6],wererediscoveredtobeShannon-bycombiningthoseofsmalllengthbasedontheChineselimit-approachingcodesoveradditivewhiteGaussiannoiseRemainderTheorem.AnAPM-LDPCcodeoflargelengthcan(AWGN)channels[9],[14].Ithasbeenwell-knownthatbeobtainedbycombiningtwoormore
7、APM-LDPCcodesofLDPCcodesperformextremelyclosetotheShannoncapacitysmallerlength.WeshowthatthegirthsoftheAPM-LDPCforsufficientlylargecodelength[1],[8],[9],[13].However,codesobtainedinthismethodarealwayslargerthanorequaltheperformanceofLDPCcodeso
