离散信道容量的迭代算法及其实现

第18卷第1期2008年1月安徽冶金科技职业学院学报JournalofAnhuiVocationalCollegeofMetallurgyandTechnologyVol.18.No.1Jan.2008辛英(山东工商学院数学与信息科学学院山东烟台264005):在简要介绍信道容量概念的基础上,简单介绍了一般信道信道容量的计算步骤,并提出它的局限性然后在其基础上详细的介绍了更为广泛的一般信道的信道容量的计算方法迭代法以及它在Java中的实现过程:信道容量;迭代算法;JAVA:TN91122:A:1672-9994(2008)01-0031-03:2007-12-22:(1979-),,,1I(X;Y)XP(x),(P(x)),C,C=max{I(X;Y)},t,C1=1tmax{I(X;Y)}(),C1,tC,,,,2,,P(x)I(X;Y)P(x),I(X;Y)r{P(a1),P(a2),!P(ar)},ri=1P(ai)=1=I(X;Y)-[ni=1P(xi)-1],p(xi)={I(X;Y)-[ni=1P(xi)-1]}p(xi)=0C:(1)mj=1p(yjxi)!j=mj=1p(yjxi)log2(yjxi),!j(2)C=log2(mj=12!j),C(3)p(yj)=2!j-C,p(yj)(4)p(yj)=ni=1p(xi)p(yjxi),p(xi)(2),,p(xi),p(xi)Cp(xi),C,p(xi),C,3,X,Y,I(X;Y)=ijp(xi)p(yjxi)lnp(yjxi)ip(xi)p(yjxi)(1)Cp(xi),I(X;Y),q(xiyj)=p(xi)p(yjxi)ip(xi)p(yjxi)(2),(2)I(X;Y)=ijp(xi)p(yjxi)lnq(xiyj)p(xi)(3),(p(yjxi)),I(X;Y)p(xi)q(xiyj),(3)():(1)p(n)(xi),iq(xiyj)=1q(xiyj),I(X;Y),I(X;Y)=C(p(n)(xi);q(n)(xiyj))=C(n,n);q(n)(xiyj)(2);q(n)(xiyj)=p(n)(xi)p(yjxi)p(n)(xi)p(yjxi)(4)(2)q(n)(xiyj),ip(xi)=1p(xi),I(X;Y),I(X;Y)=Cp(n+1)(xi);q(n)(xiyj))=C(n+1,n);p(n+1)(xi)=ejp(yjxi)lnq(n)(xiyj)iejp(yjxi)lnq(n)(xiyj)(5)(4)(5)p(n)(xi)(n=1),,(4)q(n)(xiyj);(5)p(n+1)(xi),(3)I(X;Y),I(X;Y),,I(X;Y)C:r,s,∀,p(xi)=1r(1)q(yj)=ip(xi)p(yjxi);(2)#i=ejp(yjxi)ln(p(yjxi)q(yj)),i=1,!r;(3)u=ip(xi)#i;(4)IL=log2(u),IU=log2(max#i)(5)IU-IL∀,6),p(xi)=p(xi)#iu,i=1,!r;1)(6)C=IL()4JAVAimportjava.io.*;publicclassIteration{publicstaticvoidmain(String[]args)throwsIOException{----Strings;inti=0;BufferedReaderbr=newBufferedReader(newInputStreamReader(newFileInputStream(∀diedai.txt∀)));while((s=br.readLine())!=null)i++;----String[][]r1=newString[i][];BufferedReaderbr2=newBufferedReader(newInputStreamReader(newFileInputStream(∀diedai.txt∀)));intl=0;while((s=br2.readLine())!=null){r1[l]=s.split(∀∀);l++;}double[][]r=newdouble[i][r1[0].length];System.out.println(∀:∀);for(intj=0;ji;j++){for(intk=0;kr[0].length;k+){r[j][k]=Double.parseDouble(r1[j][k]);System.out.print(r[j][k]++∀∀);}System.out.println();}Iterationt=newIteration();t.iterate(r);}#32#安徽冶金科技职业学院学报2008年第1期publicvoiditerate(double[][]r){double[]p=newdouble[r.length];double[]q=newdouble[r.length];double[]a=newdouble[r.length];doubleu=0,il=0,iu=0,e=1,c=0;do{for(inti=0;ir.length;i++)p[i]=1.0r.length;for(inti=0;ir.length;i++)for(intj=0;jr[i].length;j++)q[i]+=p[i]*r[j][i];for(inti=0;ir.length;i++)for(intj=0;jr[i].length;j++)a[i]=1;for(inti=0;ir.length;i++)for(intj=0;jr[i].length;j++)a[i]*=Math.pow(r[i][j]q[j],r[i][j]);for(inti=0;ir.length;i++)u+=p[i]*a[i];il=Math.log10(u)Math.log10(2.0);iu=Math.log10(max(a))Math.log10(2.0);c=iu-il;for(inti=0;ir.length;i++)p[i]=p[i]*a[i]u;}while(ce);System.out.println(∀:∀+il);}publicdoublemax(double[]x){adoublet=0;for(intj=0;jx.length-1;j++)for(inti=0;ix.length-1-j;i++)if(x[i]x[i+1]){t=x[i];x[i]=x[i+1];x[i+1]=t;}returnx[x.length-1];}}5diedai.txt0.50.2500.25010000100.2500.250.5,∀1,:1.2808,log25-1=1.3219,3.1%,0.11.8658,41.1%,,,∀,[1]傅祖芸信息论基础理论与应用[M∃北京:电子工业出版社,2002[2]陈运,周亮,陈新信息论与编码[M∃北京:电子工业出版社,2005[3]周萌清,信息理论基础[M∃北京:北京航空航天大学出版社,2006RealzationofTheIterationOnDiscreteChannelCapacityXINGYingAbstract:Thispaperintroducesthecomputationstepofthecommonchannel%schannelcapacitysimplyonthebasisoftheconceptionofchannelcapacity,andproposesitslimitation.Onthebasisofthis,thenelaboratelyintroducesmorewidespreadcommonchannelscapacity%scomputationalmethoditerativearithmeticanditsrealizationprocessbasedonJava.Keywords:ChannelCapacity;IterativeArithmetic;JAVA#33#总第39期辛英:离散信道容量的迭代算法及其实现