[d6dad2]: inst / huffmandict.m  Maximize  Restore  History

Download this file

215 lines (185 with data), 6.5 kB

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
## Copyright (C) 2006 Muthiah Annamalai <muthiah.annamalai@uta.edu>
##
## This program is free software; you can redistribute it and/or modify it under
## the terms of the GNU General Public License as published by the Free Software
## Foundation; either version 3 of the License, or (at your option) any later
## version.
##
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
## details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} huffmandict (@var{symb}, @var{prob})
## @deftypefnx {Function File} {} huffmandict (@var{symb}, @var{prob}, @var{toggle})
## @deftypefnx {Function File} {} huffmandict (@var{symb}, @var{prob}, @var{toggle}, @var{minvar})
##
## Builds a Huffman code, given a probability list. The Huffman codes
## per symbol are output as a list of strings-per-source symbol. A zero
## probability symbol is NOT assigned any codeword as this symbol doesn't
## occur in practice anyway.
##
## @var{toggle} is an optional argument with values 1 or 0, that starts
## building a code based on 1s or 0s, defaulting to 0. Also @var{minvar}
## is a boolean value that is useful in choosing if you want to optimize
## buffer for transmission in the applications of Huffman coding, however
## it doesn't affect the type or average codeword length of the generated
## code. An example of the use of @code{huffmandict} is
##
## @example
## @group
## huffmandict (symbols, [0.5 0.25 0.15 0.1], 1)
## @result{} @{[0], [1 0], [1 1 1], [1 1 0]@}
## huffmandict (symbols, 0.25 * ones (1,4), 1)
## @result{} @{[1 1], [1 0], [0 1], [0 0]@}
##
## prob = [0.5 0 0.25 0.15 0.1];
## dict = huffmandict (1:5, prob, 1);
## entropy (prob)
## @result{} 2.3219
## laverage (dict, prob)
## @result{} 1.8500
##
## x = [0.2 0.4 0.2 0.1 0.1];
## huffmandict (1, x, 0, true)
## @result{} @{[1 0], [0 0], [1 1], [0 1 0], [0 1 1]@}
## huffmandict (1, x)
## @result{} @{[0 1], [1], [0 0 1], [0 0 0 0], [0 0 0 1]@}
## @end group
## @end example
##
## Reference: Dr.Rao's course EE5351 Digital Video Coding, at UT-Arlington.
## @seealso{huffmandeco, huffmanenco}
## @end deftypefn
## Huffman code algorithm.
## while (uncombined_symbols_remain)
## combine least probable symbols into one with,
## their probability being the sum of the two.
## save this result as a stage at lowest order rung.
## (Moving to lowest position possible makes it non-minimum variance
## entropy coding)
## end
##
## for each (stage)
## Walk the tree we built, and assign each row either 1,
## or 0 of
## end
##
## reverse each symbol, and dump it out.
##
function cw_list = huffmandict (sym, source_prob, togglecode = 0, minvar = 0)
if nargin < 2
print_usage ();
## need to compare to 1
elseif ((sum (source_prob) - 1.0) > 1e-7)
error ("source probabilities must add up to 1.0");
endif
## need to find & eliminate the zero-probability code words.
## in practice we donot need to assign anything to them. Reasoning
## being that if_ it doesnt occur why bother saving its value anyway?
## --(Oct 9) Actually some experts in the area dont agree to this,
## and being a generic implementation we should stick to generating
## CWs for_ zero symbols. Why impose a bad implementation? --Muthu
origsource_prob = source_prob;
## sort the list and know the index transpositions. kills the speed O(n^2).
L = length (source_prob);
index = [1:L];
for itr1 = 1:L
for itr2 = itr1:L
if (source_prob(itr1) < source_prob(itr2))
t = source_prob(itr1);
source_prob(itr1) = source_prob(itr2);
source_prob(itr2) = t;
t = index(itr1);
index(itr1) = index(itr2);
index(itr2) = t;
endif
endfor
endfor
stage_list = {};
cw_list = cell (1, L);
stage_curr = {};
stage_curr.prob_list = source_prob;
stage_curr.sym_list = {};
S = length (source_prob);
for i = 1:S;
stage_curr.sym_list{i} = [i];
#cw_list{i} = "";
endfor
## another O(n^2) part.
I = 1;
while (I<S)
L = length (stage_curr.prob_list);
nprob = stage_curr.prob_list(L-1) + stage_curr.prob_list(L);
nsym = [stage_curr.sym_list{L-1}(1:end), stage_curr.sym_list{L}(1:end)];
## stage_curr;
## archive old stage list.
stage_list{I} = stage_curr;
## insert the new probability into the list, at the
## first-position (greedy?) possible.
for i = 1:(L-2)
if ((minvar && stage_curr.prob_list(i) <= nprob) || ...
stage_curr.prob_list(i) < nprob)
break;
endif
endfor
stage_curr.prob_list = [stage_curr.prob_list(1:i-1) nprob stage_curr.prob_list(i:L-2)];
stage_curr.sym_list = {stage_curr.sym_list{1:i-1}, nsym, stage_curr.sym_list{i:L-2}};
## Loopie
I = I + 1;
endwhile
if (togglecode == 0)
one_cw = 1;
zero_cw = 0;
else
one_cw = 0;
zero_cw = 1;
endif
## another O(n^2) part.
I = I - 1;
while (I > 0)
stage_curr = stage_list{I};
L = length (stage_curr.sym_list);
clist = stage_curr.sym_list{L};
for k = 1:length (clist)
cw_list{1,clist(k)} = [cw_list{1,clist(k)} one_cw];
endfor
clist = stage_curr.sym_list{L-1};
for k = 1:length (clist)
cw_list{1,clist(k)} = [cw_list{1,clist(k)}, zero_cw];
endfor
## Loopie
I = I - 1;
endwhile
## zero all the code-words of zero-probability length, 'cos they
## never occur.
S = length (source_prob);
for itr = (S+1):length (origsource_prob)
cw_list{1,itr} = -1;
endfor
#disp("Before resorting")
#cw_list
nw_list = cell (1, L);
##
## Re-sort the indices according to the probability list.
##
L = length (source_prob);
for itr = 1:(L)
t = cw_list{index(itr)};
nw_list{index(itr)} = cw_list{itr};
endfor
cw_list = nw_list;
## zero all the code-words of zero-probability length, 'cos they
## never occur.
#for itr = 1:L
# if (origsource_prob(itr) == 0)
# cw_list{itr} = "";
# endif
#endfor
endfunction
%!assert (huffmandict (1:4, [0.5 0.25 0.15 0.1], 1), {[0], [1 0], [1 1 1], [1 1 0]}, 0)
%!assert (huffmandict (1:4, 0.25*ones (1, 4), 1), {[1 1], [1 0], [0 1], [0 0]}, 0)
%!assert (huffmandict (1:4, [1 0 0 0 ]), {[1], [0 1], [0 0 0], [0 0 1]}, 0)

Get latest updates about Open Source Projects, Conferences and News.

Sign up for the SourceForge newsletter:





No, thanks