function CODE = huffman(p)
%HUFFMAN Builds a variable-length Huffman code for a symbol source.
% CODE = HUFFMAN(P) returns a Huffman code as binary strings in
% cell array CODE for input symbol probability vector P. Each word
% in CODE corresponds to a symbol whose probability is at the
% corresponding index of P.
%
% Based on huffman5 by Sean Danaher, University of Northumbria,
% Newcastle UK. Available at the MATLAB Central File Exchange:
% Category General DSP in Signal Processing and Communications.
% Copyright 2002-2004 R. C. Gonzalez, R. E. Woods, & S. L. Eddins
% Digital Image Processing Using MATLAB, Prentice-Hall, 2004
% $Revision: 1.5 $ $Date: 2003/10/26 18:37:16 $
% Check the input arguments for reasonableness.
error(nargchk(1, 1, nargin));
if (ndims(p) ~= 2) | (min(size(p)) > 1) | ~isreal(p) | ~isnumeric(p)
error('P must be a real numeric vector.');
end
% Global variable surviving all recursions of function 'makecode'
global CODE
CODE = cell(length(p), 1); % Init the global cell array
if length(p) > 1 % When more than one symbol ...
p = p / sum(p); % Normalize the input probabilities
s = reduce(p); % Do Huffman source symbol reductions
makecode(s, []); % Recursively generate the code
else
CODE = {
'1'
}; % Else, trivial one symbol case!
end;
%-------------------------------------------------------------------%
function s = reduce(p);
% Create a Huffman source reduction tree in a MATLAB cell structure
% by performing source symbol reductions until there are only two
% reduced symbols remaining
s = cell(length(p), 1);
% Generate a starting tree with symbol nodes 1, 2, 3, ... to
% reference the symbol probabilities.
for i = 1:length(p)
s{i} = i;
end
while numel(s) > 2
[p, i] = sort(p); % Sort the symbol probabilities
p(2) = p(1) + p(2); % Merge the 2 lowest probabilities
p(1) = []; % and prune the lowest one
s = s(i); % Reorder tree for new probabilities
s{2} = {s{1}, s{2}}; % and merge & prune its nodes
s(1) = []; % to match the probabilities
end
%-------------------------------------------------------------------%
function makecode(sc, codeword)
% Scan the nodes of a Huffman source reduction tree recursively to
% generate the indicated variable length code words.
% Global variable surviving all recursive calls
global CODE
if isa(sc, 'cell') % For cell array nodes,
makecode(sc{1}, [codeword 0]); % add a 0 if the 1st element
makecode(sc{2}, [codeword 1]); % or a 1 if the 2nd
else % For leaf (numeric) nodes,
CODE{sc} = char('0' + codeword); % create a char code string
end
