B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

790 INTRODUCTION TO INFORMATION THEORY
function [huffcode,n] =huf fmancode (p) ;
% input p is a probability vector consisting of
% probabi lities of source symbols x_i
if min (p) <O,
error ('Negative element cannot be in a probability vector')
return
else if abs (sum (p) -1)>1.e-12 ,
error ('Sum of input probability is not l')
return
end
[psort ,pord] =sort (p) ;
n=length (p) ;
q=p ;
for i=l :n-1
[q, l] =sort (q) ;
m ( i , : ) = [ 1 ( 1 : n - i + 1) , zeros ( 1 , i-1 ) J ;
q= [q(l)+q(2) ,q(3:end) ,1];
end
Cword=blanks (n-2) ;
Cword(n )='O';
Cword(2*n) ='l';
for il=l :n-2
Ctemp=Cword;
idxO=find (m(n- il, :)==l) *n;
Cword (l:n )=[Ctemp (idx0-n+2 :idx0 ) '0'];
Cword (n+l :2*n)= [Cword (l:n-1) '1'];
for i2=2 :il+l
idx2=find (m(n-il, :)==i2) ;
Cword (i2*n+l : (i2+l) *n) =Ctemp (n* (idx2-1)+ 1:n *idx2 ) ;
end
end
for i=l :n
idxl=find (m(l, :)==i) ;
huffcode (i,1 :n) =Cword (n* ( idxl-1)+1:idxl*n) ;
end
end
The second program, huf fmanEx . m, generates a very simple example of Huffman encoding. In
this exercise, we provide an input probability vector of length 8. The MATLAB program huf fmanEx . m
will generate the list of codewords for all the input symbols. The entropy of this source H (x) is computed
and compared against the average Huffman codeword length. Their ratio shows the efficiency of the
code.
% Matlab Program <huffmanEx .m>
% This exercise requires the input of a
% probability vector p that list all the