信息论实验作业.doc

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1、实验一信息量的计算1、基本要求：编写计算离散随机变量的熵、联合熵、条件熵、互信息的Matlab程序2、输入：一个离散的概率分布3、输出：信息量（单位比特）4、函数说明：熵e=Entropy（x）x是一个向量表示一个离散的概率分布联合熵e=JEntropy（xy）xy联合分布密度函数条件熵e=CEntropy（xy，sign）xy联合分布密度函数，sign=‘x’表示y关于x的条件概率，sign=‘y’表示x关于y的条件概率互信息e=IInfo（xy）xy联合分布密度函数%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

2、%%%%%程序：functione=Entropy(x)%熵,x是一个向量表示一个离散的概率分布x(x==0)=1;e=-sum(x.*log2(x))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%functione=JEntropy(xy)%联合熵,xy联合分布密度函数xy(xy==0)=1;e=-sum(sum(xy.*log2(xy)))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%functione=CEntropy(xy,sign)%条件熵.xy=

3、联合分布密度函数,sign=‘x’表示y关于x的条件概率x=sum(xy,2);y=sum(xy,1);ifsign=='x'e=JEntropy(xy)-Entropy(x);elseifsign=='y'e=JEntropy(xy)-Entropy(y);elsee=FALSEendend%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%functione=IInfo(xy)%互信息,xy联合分布密度函数x=sum(xy,2);y=sum(xy,1);e=log2(xy)-log2(x*y)%%%%%%%

4、%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%利用下表中的数据进行测试，结果如下：ajai01201/41/18011/1811/181/31/184/9201/187/361/411/364/91/4测试结果：>>x=[11/364/91/4]>>Entropy(x)e=1.5426>>xy=[1/41/1801/181/31/1801/187/36]>>JEntropy(xy)e=2.4144>>CEntropy(xy,'y')e=0.8717>>e=IInfo(xy)e=1.4210-1.2895-Inf-1.2

5、8950.7549-1.0000-Inf-1.00001.6374