第四讲信道信道容量与信道编码_59502584

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1、&EØÄ:1où&!&Nþ&?è±#,·uÆgÄzX&E?nïĤ2010cS1où&!&Nþ&?èSNJ11où&!&Nþ&?è&9Ù.&Nþ&Nþ(élÑÃPÁ&)&NþO?é&Ú¿é&&Nþ&?è&?è&?è½nHammingè±#,·&EØÄ:&9Ù.&Nþ1où&!&Nþ&?è?é&Ú¿é&&Nþ&?è&&:&EDÑÏ~:>C!1Å´!1n!ÈÅì!^&Ò(½Ù¦&E)?nL§ÑX−→&−→ÑÑY±#,·&EØÄ:&9Ù.&Nþ1où&

2、!&Nþ&?è?é&Ú¿é&&Nþ&?è&.âÑ/ÑÑa.Ñ/ÑÑ&Òm(½Â)()lÑlÑlÑ&(êi&)lÑëYëY&ëYëY[&âÑ!ÑÑ'XPÁ5,&ÑÑT&Ñk'—ÃPÁ&,&Ñѱc&Ñk'—kPÁ&âÑ!ÑÑ'X(½5kD(&ÃD&±#,·&EØÄ:&9Ù.&Nþ1où&!&Nþ&?è?é&Ú¿é&&Nþ&?èÑ!ÑÑÑ´ÅL§,§m'X^^VÇÝL«.élÑÃPÁ&ÑXAX={a1,a2,···,aK}ÑÑYAY={b1,b2

3、,···,bJ}ÑÑÑ'XQQ={q(bj

4、ak)}K×J↔&·¤'%´:lÑÑà±'uÑà&Eþ,=öp&E.±#,·&EØÄ:&9Ù.&Nþ1où&!&Nþ&?è?é&Ú¿é&&Nþ&?è&Nþ1C,limmaxI(X1X2···XN;Y1Y2···YN)N→∞N¤kU&35?XÛ¦?½½½nnn:&Ñ!ÑÑ©Ox=(x1x2···xN)Úy=(y1y2···yN),KélÑÃPÁ&kXNI(X1X2···XN;Y1Y2···YN)≤I(Xn;Yn)n=1&´lÑÃPÁ,þãت

5、”=”.±#,·&EØÄ:&9Ù.&Nþ1où&!&Nþ&?è?é&Ú¿é&&Nþ&?èy²:lÑÃPÁ&÷vYNq(y

6、x)=q(y1y2···yN

7、x1x2···xN)=q(yn

8、xn)n=1I(X1X2···XN;Y1Y2···YN)=I(X;Y)=H(Y)−H(Y

9、X)H(Y)=H(Y1Y2···YN)=H(Y1)+H(Y2

10、Y1)+H(Y3

11、Y1Y2)+···+H(YN

12、Y1Y2···YN−1)XN≤H(Yn)n=1±#,·&EØÄ:&9Ù.&Nþ1où&!&Nþ&?è?é&Ú¿é&

13、&Nþ&?èqXH(Y

14、X)=−P(x1···xNy1···yN)logq(y1···yN

15、x1···xN)x,yXYN=−P(x1x2···xNy1y2···yN)log[q(yn

16、xn)]x,yn=1XNX=−P(x1x2···xNy1y2···yN)logq(yn

17、xn)n=1x,yXNXX=−logq(yn

18、xn)[P(x1···xNy1···yN)]n=1xn,ynxi,yji,jÑØnXNXXN=−logq(yn

19、xn)P(xnyn)=H(Yn

20、Xn)n=1xn,ynn=1XN±#,·&EØÄ:∴I(X;Y)≤I(Xn;Yn

21、)&9Ù.&Nþ1où&!&Nþ&?è?é&Ú¿é&&Nþ&?è&lÑÃPÁ,=YNP(x)=P(xn)n=1XP(y)=P(x)q(y

22、x)xX=[P(x1)···P(xN)q(y1

23、x1)···q(yN

24、xn)]x1,···,xNXX=[P(x1)q(y1

25、x1)]·[P(x2)q(y2

26、x2)]x1x2X···[P(xN)q(yN

27、xN)]xNYN=P(yn)n=1±#,·&EØÄ:&9Ù.&Nþ1où&!&Nþ&?è?é&Ú¿é&&Nþ&?è=&ÑÑ´ÃPÁXN∴H(Y)=H(Yn

28、)n=1dþ¡Øª”=”Ò.XN1(Ø:C≤limmaxI(Xn;Yn)N→∞N¤kU&n=1±#,·&EØÄ:&9Ù.&Nþ1où&!&Nþ&?è?é&Ú¿é&&Nþ&?è¹e,·Äð&(¢SA^&ÑÄþÑ´ð&½wð)d∀n,I(Xn;Yn)Ñ,PI(X¯;Y¯)þªC≤maxI(X¯;Y¯)¤kð&éulÑÕá&,k1C≥limmaxI(X1X2···XN;Y1Y2···YN)N→∞N¤kÃPÁ&XN1=limmaxI(Xn;Yn)N→∞N¤kÃPÁ&n=1=maxI(X¯;Y¯)¤kÃPÁ&±#

29、,·&EØÄ:&9Ù.&Nþ1où&!&Nþ&?è?é&Ú¿é&&Nþ&?èé?ð&X5`,XKXJq(b

30、a)jkI(X¯