example8_1_to_8_3.m

these are the Mtlab functions to plot the figures in the book Communication system (by Haykin)

%Huffman coding example  
%ch7-huffman.m

Q=[      0.6250    0.3750    0.3750    0.3750
    0.1875    0.3125    0.1875    0.1875
    0.1250    0.1875    0.3125    0.1250
    0.0625    0.1250    0.1250    0.3125]
    

 %Q(i,j) is prob(i|j)
 
 %use [W,D]=eig(A) to determine the eigenvector corresponding to eigen value 1
 %then normalize the vector to sum 1 
 
p =[
    0.5000
    0.2143
    0.1703
    0.1154]
 
 %p(i)=prob(i);
 
 P2=Q*diag(p);
 %P2(i,j)=prob(i,j);
 
%P2 =
%    0.3125    0.0804    0.0639    0.0433
%    0.0937    0.0670    0.0319    0.0216
%    0.0625    0.0402    0.0532    0.0144
%    0.0312    0.0268    0.0213    0.0361
 
 %first order entropy
 H1=-sum(p.*log2(p));
 %H1=1.7707
 %2nd order entropy;
 H2=-sum(sum(P2.*log2(P2)));
 %H2=3.4629; H2/2=1.73145
 
 %conditional entropy
 for (j=1:4)
    HC(j)=-sum(Q(:,j).*log2(Q(:,j)));
 end;
 
 %HC=   1.5016    1.8829    1.8829    1.8829 
 HCT=sum(p'.*HC);
 %HCT=1.6922