Channel polarization

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1、IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.55,NO.7,JULY20093051ChannelPolarization:AMethodforConstructingCapacity-AchievingCodesforSymmetricBinary-InputMemorylessChannelsErdalArıkan,SeniorMember,IEEEAbstract—Amethodisproposed,calledchannelpolarization,A.Preliminariestoconstructco

2、desequencesthatachievethesymmetriccapacityWewritetodenoteagenericB-DMCwithofanygivenbinary-inputdiscretememorylesschannel(B-DMC).Thesymmetriccapacityisthehighestrateachiev-inputalphabet,outputalphabet,andtransitionprobabilitiesablesubjecttousingtheinputlettersofthechannel

3、withequal.Theinputalphabetwillalwaysbeprobability.Channelpolarizationreferstothefactthatitispos-,theoutputalphabetandthetransitionprobabilitiesmaysibletosynthesize,outofindependentcopiesofagivenB-DMCbearbitrary.Wewritetodenotethechannelcorresponding,asecondsetofbinary-in

4、putchannelstousesof;thus,withsuchthat,asbecomeslarge,thefractionofindicesforwhich.isnearapproachesandthefractionforwhichisnearapproaches0.ThepolarizedchannelsGivenaB-DMC,therearetwochannelparametersofpri-arewell-conditionedforchanne

5、lcoding:oneneedonlymaryinterestinthispaper:thesymmetriccapacitysenddataatratethroughthosewithcapacitynearandatratethroughtheremaining.Codesconstructedonthebasisofthisideaarecalledpolarcodes.Thepaperprovesthat,givenanyB-DMCwithandanytargetrate,thereexistsaseque

6、nceofpolarcodessuchthathasblock-lengthandtheBhattacharyyaparameter,rate,andprobabilityofblockerrorundersuc-0cessivecancellationdecodingboundedasindependentlyofthecoderate.Thisperformanceisachievablebyencodersanddecoderswithcomplexityforeach.Thesepara

7、metersareusedasmeasuresofrateandreliability,IndexTerms—Capacity-achievingcodes,channelcapacity,channelpolarization,Plotkinconstruction,polarcodes,Reedrespectively.isthehighestrateatwhichreliablecommu-Muller(RM)codes,successivecancellationdecoding.nicationispossibleacrossusingt

8、heinputsofwithequalfrequency.isanupperboundontheprobabilityof