%ELG5126
%Huffman coding example from Lecture 4
clear all, close all;
%probability vector
p = [.25 .2 .2 .18 .09 .05 .02 .01];
%first order entropy
H_1 = sum(-p .* log2(p));
%define the symbols to be the integers from 1 to 8
sym = 1:8;
%
%Use the huffmandict routine from the communications toolbox to get both a
%Huffman code and the average codeword length. 
%If you double-click DICT in the workspace, you can see the codewords in
%the Variable Editor.
%
[DICT, AVGLEN] = huffmandict(sym,p);
%
%Shannon codeword lengths and average codeword length
ell_i_shann = ceil(-log2(p));
ell_shann = sum(p.*ell_i_shann);