第五章 无失真信源编码定理.

1、第五章第五章 无失真信源编码定理无失真信源编码定理 ,21qsss,:21rxxxX:il,21qWWWis)(21iliiiixxxW Xxki iiiiiWsssSN )(21Sski iWiWis1 ,0 XjijiWWss 时时，当当jijiWWss 时时，当当 rxxxX,:21ix)(21NiiiiWWWB qiiiqiNN,2, 1,2, 121 4321,ssss,44163132121112ssssssssS 1 2 3 4 5 6 16 0011 WW00121 WW000131 WW011141 WW01012 WW010122 WW11111144 WW,4416313

2、212111WWBWWBWWBWWBB 1s2s1s1s3sqsss,21rxxx,21llrq 3, 2,6 lrq则2, 2,4 lrq则则NqNq ,21rlqNloglog rqNlloglog rqlloglog NllNrq )()()()()(43214321sPsPsPsPsssssPS1)(41 iisP0)|( ijssP1)|()|()|()|(43342112 ssPssPssPssP )()()()()(34431221344312212ssPssPssPssPssssssssssPSji2S1642 Nq2 llNl 111 qiip qqpppssssPS,)(2

3、121 )(,),(),(,)(2121NNqqNpppPS NkiNkiikkpsPP11)()( NkiNkiiikksIpPI11)(log)(log)( NkiNkiiikksIpPI11)(log)(log)( )()()()(1SHNsIESHIENkiNik 211222loglog)()()()(iqiiqiiiiiippppNSHsIENsIDNID q )(iID nXXX21niiXn11Nsss21is)(sPNiiiissssssN21)(21 )(log1)(log121NiiiisssPNPN )(SH)()()(log1)(log)(log)(log1)(log

4、12121SHsIEsPNsPsPsPNsssPNiSiiiiiiiNN0 1)()(lim SHNIPiN11XExNNii i NIi)( )(SHNqi )(SH )()(SHNIi )()(logSHNPii NS i NG )()(:SHNIGiiN NG )()(:SHNIGiiNNNNNNSGGGG NiG )()(2)(2 SHNiSHNP|NG NG )()(2|2)1( SHNNSHNG, 0, 0 )(,1)(NNGPGP )()(SHNIPi222)()()()()( NsIDNsIDNNIDiii 0NN 1)()(SHNIPi 2)( XDXP 2)()(| )()

5、(| NIDNSNHIPiiX )()(SHsIEi 0)(lim),(lim2 NsIDNiNN )()(logSHNPi )(2)(SNHiP NG N)(iP )(2SNH N)(2|SNHNG )(log)(22| SHqNNSHNNNqqG0)(log,log)( SHqqSH0, NNG NNqS NG NG )(2 SHN )(2SNH 1)(NGP l0 )(SHrSHNllog)( rSHNllog2)( rqNlloglog qSHlog)( qSHlog)(l)(2| SHNlNlrGrrSHNllog)( 2)(),()( NsIDNGPPiNE |22)(NSHNlG

6、r 2 r )(SHNl)(2)1 (| SHNNG1, EPNNG )()(1lim)(lim21SHXXXHNXHNNNN )(SH rSHNllog)( rSHNllog2)( rSHNllog)( )(loglog)(SNHrlrSHNl l )(logSHrNlrNlRlog R1log)()( rNlSHRSH 0)()( SHSH)(1SH 222)1()()( SHsIDNi 2)( NsIDPiE 22)()( iisIDNNsID )(1SH 222)1()()( SHsIDNi8113. 041,43)( HSH96. 0 510 4143)(21sssPS7522210

7、12. 41004. 096. 0.8113. 04710. 0 N 4710. 08113. 034log434log41)()(log)(2222221 SHppsIDiiii奇异码奇异码非奇异码非奇异码唯一可译码唯一可译码即时码即时码所有码所有码iilrrlll,21rxxxX qWWW,21qlll,2111 qilirNr)(Nii iNr iilNiril qNqilNrri 111 qilir11 qiliriiFF 例例 siCF1F2F3F4F5s1as2cs3adds4abbbbs5badads6debebbs7bbcdecdedebcde,21qsssS ,21qWWWC

8、 qlll,21)()(iiWPsP iqiilsPL 1)(LSHXH)()( ( ) ()H SRH XtLLRL1log)(log)( rSHLrSHrSHlog)(LrLSHlog)( qiiiqiiilsPrsPsP11)(log)(log)(qiliqiiiirsPsPsP11log)()(log)(0)(log)(1 qiliiirsPsPilirsP )()(1log)(loglog)(logiririisPsPrsPl )()(是正整数是正整数imimrsPi )(1logirisPl1log)(log)( rSHLrSH)()(log)(log)(log)(log)(11SHsPsPrsPsPrSHrirqiiiqii 1)()( SHLSHrrNS)(NSHNrSHNLrSHN1log)(log)( NSHNLSHrNr1)()( )(limSHNLrNN iqiiNNPL 1)(i i 1)()( NrNNrSHLSH1)()( SNHLSNHrNrNSHNLSHrNr1)()( NrSHNLrSHN1log)(log)( NNLLN )(SHrrHNLNNloglim rNLRNlog NrSHrNLSHNlog)(log)( )/()(符符号号比比特特LSHR ,log)(rSHL rLSHlog)( rRlog LSH