结果图信源熵实验程序：clc; close all; clear;linwidd=1fontt=20p0=0; pd=1; N=20p=linspace(p0,pd,N);I=-log2(p);plot(p,I,'k');title('I=-log2(p)函数图');xlabel('p');ylabel('I');clc; close all; clear;linwidd=1fontt=20p0=0; pd=1; N=20p=linspace(p0,pd,N);H=-p.*log2(p)-(1-p).*log2(1-p);plot(p,H,'k');title('H=-p.*log2(p)-(1-p).*log2(1-p)函数图');xlabel('p');ylabel('H');信道容量实验程序：clc; close all; clear;linwidd=1fontt=20p0=0; pd=1; N=20p=linspace(p0,pd,N);r=4c=log2(r)+(1-p).*log2(1-p)+p.*log2(p/(r-1));plot(p,c,'k');title('强对称信道容量数值模拟图');有噪信道编码--费诺不等式程序：结果图clc;close all;clear;r=3;p0=0.00001;pd=0.99999;N=2000;p=linspace(p0,pd,N);q=1-p;H=-p.*log2(p)-q.*log2(q);hold onHH=H+p.*log2(r-1)title('费诺不等式示意图');box onxlabel('PE');ylabel('H(X/Y)');plot(p,HH,'k:')hold onhold onfill([p,1],[HH,0],[0.6,0.6,0.6])stem((r-1)/r,1.59,'--.r')text(0.66,1.6,'最大值')香农编码程序：clc;clear all;close all;p=[0.2 0.19 0.18 0.17 0.15 0.1 0.01]; if sum(p)<1||sum(p)>1error('输入概率不符合概率分布')end[p index]=sort(p,'descend');n=length(p);pa=zeros(n,1);for ii=2:npa(ii)=pa(ii-1)+p(ii-1);endk=ceil(-log2(p));%码字长度计算c=cell(1,n);%生成元胞数组，用来存不同长度的码字for ii=1:nc{ii}='';tmp=pa(ii);for jj=1:k(ii)tmp=tmp*2;if tmp>=1tmp=tmp-1;%c{ii}{jj}='1';c{ii}=[char(c{ii}),'1']; else%c{ii}{jj}='0';c{ii}=[char(c{ii}),'0']; endendend c(index)=c;%换回原来的顺序codelength=zeros(1,n);%码长初始化for ii=1:nfprintf(['第',num2str(ii),'个消息对应为']);disp(c{ii});%显示码字codelength(ii)=length(c{ii});%endn_average=sum(codelength.*p) %平均码长fprintf('平均码长为');disp(n_average);H=-sum(p.*log2(p));fprintf('信源熵');disp(H);x=H/(n_average.*log2(2))fprintf('编码效率');disp(x);figureh=stem(1:n,codelength);%axis([0 n+1 0 n+1]);set(h,'MarkerFaceColor','blue','linewidth',2)实验结果结果图第1个消息对应为000第2个消息对应为001第3个消息对应为011第4个消息对应为100第5个消息对应为101第6个消息对应为1110第7个消息对应为1111110n_average = 3.1400平均码长为 3.1400信源熵 2.6087x =0.8308编码效率 0.8308费诺编码程序：endfor rr=2:2:needgroupnum*2index2=index_aftergroup(rr,:);for ii=index2(1):index2(2)c{ii}=[char(c{ii}),'1']; endendflag=0;index_p=[];for rr=1:needgroupnum*2indextmp=index_aftergroup(rr,:); if(indextmp(2)-indextmp(1)+1>1) flag=1;index_p=[index_p;indextmp]; endendjj=jj+1;endc(index)=c;codelength=zeros(1,N);for ii=1:Nfprintf(['第',num2str(ii),'个消息对应为']);disp(c{ii});codelength(ii)=length(c{ii}); endn_average=sum(codelength.*p)fprintf('平均码长为');disp(n_average);H=-sum(p.*log2(p));fprintf('信源熵');disp(H);x=H/(n_average.*log2(2))fprintf('编码效率');disp(x); figureh=stem(1:N,codelength);axis([0 N+1 0 N+1]);set(h,'MarkerFaceColor','blue','linewidth',2)endfunction index_aftergroup=func_group(p,index_p)index=index_p(1):index_p(2);n=length(index);p0=p(index);sump0=sum(p0);half_sump0=sump0/2;for ii=1:n-1tmpsum=sum(p0(1:ii));if abs(tmpsum-half_sump0)<=abs(tmpsum-half_sump0+p0(ii+1))index_aftergroup=[index(1) index(ii);index(ii+1) index(n)]; break;endendend实验结果结果图第1个消息对应为00第2个消息对应为010第3个消息对应为011第4个消息对应为10第5个消息对应为110第6个消息对应为1110第7个消息对应为1111n_average = 2.7400平均码长为 2.7400信源熵 2.6087x =0.9521编码效率 0.9521霍夫曼编码程序：clc;clear all;close all; A=[0.4 0.2 0.2 0.1 0.1]; A=sort(A,'descend');T=A;[m,n]=size(A);B=zeros(n,n-1);B(:,1)=T;r=B(n,1)+B(n-1,1);T(n-1)=r; T(n)=0;T=sort(T,'descend');t=n-1;for j=2:n-1B(1:t,j)=T(1:t);K=find(T==r);%B(n,j)=K(end);B(n,j)=K(1);r=(B(t-1,j)+B(t,j));T(t-1)=r;T(t)=0;T=sort(T,'descend');t=t-1;endB;ENDc1=sym('[1,0]');ENDc=ENDc1;t=3;d=1;for j=n-2:-1:1for i=1:t-2if i>1&&B(i,j)==B(i-1,j)d=d+1;elsed=1;endB(B(n,j+1),j+1)=-1;temp=B(:,j+1);x=find(temp==B(i,j));ENDc(i)=ENDc1(x(d));endy=B(n,j+1);ENDc(t-1)=[char(ENDc1(y)),'1']; ENDc(t)=[char(ENDc1(y)),'0'];t=t+1;ENDc1=ENDc;endA%排序后的原概率序列ENDc%编码结果for i=1:n[a,b]=size(char(ENDc(i)));L(i)=b;endavlen=sum(L.*A)%平均码长selen=(L-avlen).^2%?mselen=sum((selen).*A)%码长均方差H=-A*(log2(A'))%?P=H/avlen%?figure;subplot(2,1,1)h=stem(1:n,selen);%axis([0 n+1 0 max(selen)+0.1]);set(h,'MarkerFaceColor','blue','lin ewidth',2)xlabel('信源向上排');ylabel('方差值selen');hold onplot(0:n+1,mselen*ones(1,n+2),'r',' linewidth',2);hold offlegend('每个信源码长与平均码长的方差','码长均方差');A=[0.4 0.2 0.2 0.1 0.1];A=sort(A,'descend');T=A;[m,n]=size(A);B=zeros(n,n-1); B(:,1)=T;r=B(n,1)+B(n-1,1);T(n-1)=r;T(n)=0;T=sort(T,'descend');t=n-1;for j=2:n-1B(1:t,j)=T(1:t);K=find(T==r);B(n,j)=K(end);%B(n,j)=K(1);r=(B(t-1,j)+B(t,j));T(t-1)=r;T(t)=0;T=sort(T,'descend');t=t-1;endB;ENDc1=sym('[1,0]');ENDc=ENDc1;t=3;d=1;for j=n-2:-1:1for i=1:t-2if i>1&&B(i,j)==B(i-1,j)d=d+1;elsed=1;endB(B(n,j+1),j+1)=-1;temp=B(:,j+1);x=find(temp==B(i,j));ENDc(i)=ENDc1(x(d));endy=B(n,j+1);ENDc(t-1)=[char(ENDc1(y)),'1'];ENDc(t)=[char(ENDc1(y)),'0'];t=t+1;ENDc1=ENDc;endA%排序后的原概率序列ENDc%编码结果for i=1:n[a,b]=size(char(ENDc(i)));L(i)=b;endavlen=sum(L.*A)%平均码长selen=(L-avlen).^2%?mselen=sum((selen).*A)%码长均方差H=-A*(log2(A'))%?P=H/avlen%?subplot(2,1,2)h=stem(1:n,selen);%axis([0 n+1 0 max(selen)+0.1]);set(h,'MarkerFaceColor','blue','linewidth',2)xlabel('信源向下排');ylabel('方差值selen');hold onplot(0:n+1,mselen*ones(1,n+2),'r','linewidth',2);hold offlegend('每个码长与平均码长的方差','码长均方差');实验结果A = 0.4000 0.2000 0.20000.1000 0.1000ENDc =[ 11, 1, 0, 101, 100]avlen = 1.8000selen = 0.0400 0.6400 0.64001.4400 1.4400mselen =0.5600H =2.1219P =1.1788A =0.4000 0.2000 0.20000.1000 0.1000ENDc =[ 0, 10, 111, 1101, 1100]avlen =2.2000selen = 1.4400 0.0400 0.64003.2400 3.2400mselen =1.3600H =2.1219P =0.9645结果图。