/usr/share/octave/packages/communications-1.1.1/golombenco.m is in octave-communications-common 1.1.1-1.
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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 | ## 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} {} golombenco (@var{sig}, @var{m})
##
## Returns the Golomb coded signal as cell array.
## Also total length of output code in bits can be obtained.
## This function uses a @var{m} need to be supplied for encoding signal vector
## into a golomb coded vector. A restrictions is that
## a signal set must strictly be non-negative. Also the parameter @var{m} need to
## be a non-zero number, unless which it makes divide-by-zero errors.
## The Golomb algorithm [1], is used to encode the data into unary coded
## quotient part which is represented as a set of 1's separated from
## the K-part (binary) using a zero. This scheme doesnt need any
## kind of dictionaries, it is a parameterized prefix codes.
## Implementation is close to O(N^2), but this implementation
## *may be* sluggish, though correct. Details of the scheme are, to
## encode the remainder(r of number N) using the floor(log2(m)) bits
## when rem is in range 0:(2^ceil(log2(m)) - N), and encode it as
## r+(2^ceil(log2(m)) - N), using total of 2^ceil(log2(m)) bits
## in other instance it doesnt belong to case 1. Quotient is coded
## simply just using the unary code. Also accroding to [2] Golomb codes
## are optimal for sequences using the bernoulli probability model:
## P(n)=p^n-1.q & p+q=1, and when M=[1/log2(p)], or P=2^(1/M).
##
## Reference: 1. Solomon Golomb, Run length Encodings, 1966 IEEE Trans
## Info' Theory. 2. Khalid Sayood, Data Compression, 3rd Edition
##
## An exmaple of the use of @code{golombenco} is
## @example
## @group
## golombenco(1:4,2) #
## golombenco(1:10,2) #
## @end group
## @end example
## @end deftypefn
## @seealso{golombdeco}
function [gcode,Ltot]=golombenco(sig,m)
if ( nargin < 2 || m<=0)
error('usage: golombenco(sig,m); see help');
end
if (min(sig) < 0)
error("signal has elements that are outside alphabet set ...
. Accepts only non-negative numbers. Cannot encode.");
end
L=length(sig);
quot=floor(sig./m);
rem=sig-quot.*m;
C=ceil(log2(m));
partition_limit=2**C-m;
Ltot=0;
for j=1:L
if( rem(j) < partition_limit )
BITS=C-1;
else
rem(j)=rem(j)+partition_limit;
BITS=C;
end
Ltot=Ltot+BITS+1;
golomb_part=zeros(1,BITS);
%
% How can we eliminate this loop?
% I essentially need to get the binary
% representation of rem(j) in the golomb_part(i);
% -maybe when JWE or someone imports dec2binvec.
% This does MSB -> LSB
for i=BITS:-1:1
golomb_part(i)=mod(rem(j),2);
rem(j)=floor(rem(j)/2);
end
%
%actual golomb code: sandwich the unary coded quotient,
%and the remainder.
%
gcode{j}=[ones(1,quot(j)) 0 golomb_part];
end
Ltot=sum(quot)+Ltot;
return
end
%!
%! assert(golombenco(3:5,5),{[0 1 1 0],[0 1 1 1],[1 0 0 0 ]})
%! assert(golombenco(3:5,3),{[1 0 0] , [1 0 1 0],[1 0 1 1]})
%!
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