信道极化和极化码---版本2-针对学生

极化码(Polarcodes)达到信道容量的编码方案黄志亮[e-mail]讨论组安排1.赵頔2.汪宇3.左德遥4.张施怡基本要求：1.做ppt2.外行也能明白3.讨论前一到两天把ppt发给所有人讨论内容：内容不限1.可以是自己所做的工作2.可以是阅读某篇或几篇文章的心得3.可以近期所看书籍的心得4.可以是近期碰到的问题？戚河平？姚松林？俞泓帆分组待定分组和顺序TheRoadtoChannelCapacityHammingGolayReed-Muller...1950sBCHReed-Solomn...1960sListdecoding1997,SudanConvolutionalcodes1950s,EliasSequentialdecoding,WozenraftThresholddecoding,MassayViterbialgorithm,Viterbi1960sand1970sDecodingtechniqueforconvolutioalcodesEnding...Turbocodes1993,Berrou,Glavieux,andThitimajshimaLDPCcodes1963,Gallager1996,MackayandSpielmanindepentrediscoveryWithin1dB2009,ErdalArikanCapacity-achievingcodingPolarcodesChannelCapacity:C1948,ClaudeShannonClassiccoding:farfromCModerncoding:within1dBtoCAlgebraticcodingProbabilisticcodingModerncoding信道极化和极化码代表文章：ErdalArikan,ChannelPolarization:AMethodforConstructingCapacity-AchievingCodesforSymmetricBinary-InputMemorylessChannels,IEEETrans.onInformationTheory,vol.55,no.7,pp.3051-3073,July2009.由于这篇文章获得的奖励：1.The2010IEEEInformationTheoryPaperawardispresentedtoErdalArikan.2.KadirHasOutstandingAchievementAwardispresentedtoErdalArikanforaninventionthatanswers60-year-oldunsolvedproblemininformationtheoryandcommunicationengineering.3.TheInstituteofElectricalandElectronicsEngineers(IEEE)hasnamedProf.ErdalArıkananIEEEFellowforhisextraordinaryworkincontributionstocodingtheory.4.WecongratulateProf.ErdalArıkanwhoreceivedtheprestigious2013IEEEW.R.G.BakerAwardforhiscontributiontoinformationtheory.ErdalArikan，BorninAnkara,Turkey,in1958.B.S.degreefromCaliforniaInstituteofTechnology.S.M.andPh.d.degreesfromtheMassachusettsInsitituteofTechnology.极化码意义极化码（PolarCodes）信息论和编码领域顶级期刊(IEEETransonIT)2010的最佳论文奖某种程度上说，完成了自信息论提出60年来信道编码理论家们的梦想近十多来信息论和编码领域最激动人心的工作在各种不同的场景下，渐进性能达到香农限，并且有着低的复杂度ErdalArikan和我信道：概率模型-达到容量一信道信道XY有线、无线、光纤硬盘读取、...一般模型：信道信道XY信道转移概率P(y|x)离散信道：有限集合有限集合信道信道XY加性白高斯噪声二进制输入高斯信道：{0,1}20iiiiYXZZN,(,)非常好的模型信道：信道举例-达到容量二二进制对称信道BSC(p)XY0101pp1p1p二进制高斯信道BiAWGN(Eb/N0)20iiiiYXZZN,(,)(SNR=Eb/N0)Eb/N00.188dBC0.5,Eb/N01.628dBC0.75，，()CmaxI(;)111log(1)log1pxXYpppp信道编码定理-达到容量三码率：R=K/N，误码率：Pe信道容量：C=maxp(x)I(X;Y)（bitspertransmission）（二进制输入）信道编码定理：无差错传输条件下（Pe=0），最大可达码率为CEb/N0=0.188dB，C=0.5：Eb/N0=0.188dB的BiAWGN信道，无差错传输条件下，无论如何设计编码器和译码器，R最大只能到0.5。汉明码LDPC码极化码…LDPC码性能展示-达到容量四Frompaper:YuKou,ShuLin,“Low-DensityParity-CheckCodesBasedonfinitegeometries：ARediscoveryandNewResults”,IEEETrans.Infor.Theory,Vol47,No7,Nov2001极化码-达到容量五Frompaper:ErdalArikan,ChannelPolarization:AMethodforConstructingCapacity-AchievingCodesforSymmetricBinary-InputMemorylessChannels,IEEETrans.onInformationTheory,vol.55,no.7,pp.3051-3073,July2009.ErdalArikan利用信道极化现象，从理论上严格证明了如下结论：对于任意的二进制离散无记忆对称（B-DMS）信道，当码长趋向于无穷时，极化码可以达到信道容量（也即误码率趋向于零时，其码率R可以任意接近信道容量C），并且有着低的编译码复杂度。Stateoftheart(polarcodes)极化码和当前的最先进的技术有着相当或更好的性能。Frompaper:IdoTalandAlexanderVardy,“ListDecodingofPolarcodes”,IEEETrans.Infor.Theory,Vol61,No5,May2015.极化码研究现状：国内研究（1）北京邮电大学1.K.Chen,K.Niu,andJ.R.Lin,“Listsuccessivecancellationdecodingofpolarcodes,”Electron.Lett.,vol.48,no.9,pp.695-697,Apr.2012.2.K.NiuandK.Chen,“Stackdecodingofpolarcodes,”Electron.Lett.,vol.48,no.12,pp.500-501,Jun.2012.3.K.NiuandK.Chen,“CRC-aideddecodingofpolarcodes,”IEEECommun.Lett.,vol.16,no.10,pp.1668-1671,Oct.2012.4.K.Chen,K.Niu,andJ.R.Lin,“Improvedsuccessivecancellationdecodingofpolarcodes,”IEEETrans.Commun.,vol.61,no.8,pp.3100-3106,Aug.2013.5.“Beyondturbocodes:Rate-compatiblepunturedpolarcodes.”ICC20136.国家自然科学基金面上项目：信道极化码设计与优化研究2012.1-2015.12极化码研究现状：国内研究（2）南京邮电大学1.Polarlattices:whereArikanmeetsForney.ISIT20132.Ontheanalysisofmultiplicative-repetitioncodesandpolarcodesoverbinaryerasurechannels.WCSP20123.Cooperativecodingschemeusingpolarcodes.2012ICCSNT4.Performanceofpolarcodesonwirelesscommunicationchannels.ICCT20125.Polarcodesanditsapplicationinspeechcommunications.WCSP20116.Encryptedpolarcodesforwiretapchannel.2012ICCSNT7.DesignsofBhattacharyyaparameterintheconstructionofpolarcodes.2011WiCOM极化码研究现状：国内研究（3）中南大学1.Anovelchannelpolarizationonbinarydiscretememorylesschannels.2010ICCS（4）北京航空航天大学1.Anovelrate-adaptivedistributedsourcecodingschemeusingpolarcodes.2013,CommunicationsLetters,IEEE（5）浙江大学1.OnthepolarcodesforMIMO.WCSP20132.PolarcodewithBlock-lengthN=3n.WCSP2012（6）华为公司1.Anadaptivesuccessivecancellationlistdecoderforpolarcodeswithcyclicredundancycheck.2012,CommunicationsLetters,IEEE极化码研究现状：国内研究（7）浙江师范大学1.Z.L.Huang,C.J.DiaoandM.Chen,“LatencyReducedMethodforModifiedSuccessive-CancellationDecodingofPolarCodes”,ElectronicsLetters,Vol.48,No.23,pp.1505-1506,Nov.2012.2.ZhiliangHuang,ChunjuanDiao,JianxinDai,ChunjiangDuanmu,XiaWuandMingChen,“AnImprovementofModifiedSuccessive-CancellationDecoderforPolarCodes”，IEEECommunicationsLetters.20133.ZhiliangHuang,ChunjuanDiao,andMingChen,“MultipleCandidatesSuccessive-CancellationDecodingofPolarCodes”,（WCSP’2012）,Huangshan,China.4.黄志亮，陈明，极化码的编译码方法研究，[博士学位论文]，东南大学，20135.国家自然科学青年基金项目：高维核矩阵信道极化码设计和译码算法优化2015.1-2017.12极化码研究现状：国外研究2EPFL：洛桑联邦理工学院瑞士RüdigerUrbanke:Dr.UrbankeisarecipientofaFulbrightScholarship.Heisaco-authorofthebook“ModernCodingTheory”p