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1、Chapter8TrellisandGraphBasedCodesThemaincontentofThemaincontentofChapter8Chapter8Trellisbasedcodes:ConvolutionalcodesTurbocodesTurbocodesGraphbasedcodes:LDPCcodesForthesecodessoftdecisiondecodingisForthesecodes,softdecisiondecodingispossibleandnearchannelc
2、apacityperformanceisachievable.8-1TheStructureofConvolutionalCodes(CC)k，n，KThefunctiongenerators：g1=[100],g2=[101],g3=[111]Or，（4,5,7）Eachistheimpulseresponsefromtheinputsofcorrespondingfunctiongeneratortoitsoutput.Fig8.1-2,K=3,k=1,n=3,convolutionalcoderWhe
3、nththieinputttthtotheencoderiithifstheinformationsequence,thethreeoutputareu(1)cu=∗g1(2)cu=∗g2(3)cu=∗g3(1)(2)(3)(1)(2)(3)ccccccc=(111222,,,,,....)InthetransformdomainD,whereDdenotesthe-1unitdelayandD=z,g()1D=12g()1DD=+22g()1DD=++D3∞iu()Du=∑iDi=0Theoutputtr
4、ansformsare(1)c()DDDDD=u()()gD1(2)c()DD=u()()gD2(3)c()DD=u()()gD,3ThetransformoftheencoderoutputThetransformoftheencoderoutputc::(1)3(2)32(3)3c()c()D=+DDDDDc()+c()Duetodelay!Duetointerleaving!Duetointerleaving!Example8.1-1u=(100111)345uD()1=+++DDDgD()1=12g
5、()DD=1+212gD()1=++DD3input(1)345cDuDgD()()()1==+DDD++12(2)23467cDuDgD()()()1==+DDDDD++++2output(3)2357cDuDgD()()()1==+++++DDDDD33(1)3(2)32(3)3cDcD()()=++DcD()DcD()=Fi81Fig8.1-3CCih3,CCwith257891011=1+D+D+D+D+D+D+D+D+K=1,k=2,n=312131517192223+D+D+D+D+D+D+Dc
6、=()1110010111111101010100118.1-1Tree，Trellis，andStateDiagramsThreealternativemethhdodstodescribeaCC:(()1)Treediagram:Fig8.1-5with8.1-2,repeatafterKstages;(2)Trellisdiagram:Fig8.1-6with8.1-2,steadfdystatesafterKKstages.SttStatesmeansthestttatesofffit(Kfirst
7、(K-1)tht1)thstagesofshiftregistersofshiftregisters.Fig8.1-2,K=3,k=1,n=3,convolutionalcoder8.1-6TrellisdiagramK3k1K=3,k=1,n=33GenerallyforaGenerallyforaconvolutionalcode:1.Thenumberofstates(nodes)is2k(K-1);2.Foreachnodewehave2kbranchesin,2kbranchesout;3.For
8、eachstagewehave2k(K-1)2k=2kKpathmetitricsandd22k(K-1)survivorswithVitbiViterbidecodingalgorithmdecodingalgorithm.(3)Statediagram:Fig8.1-7for8.1-2818.1-7statediagram7statediagramK=3,k=1,n=3•Fork＞1,Fig8.1-3asan
