/usr/share/octave/packages/communications-1.2.0/golombenco.m is in octave-communications-common 1.2.0-1build1.
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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 | ## 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 doesn't 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 doesn't belong to case 1. Quotient is coded
## simply just using the unary code. Also according 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 example of the use of @code{golombenco} is
## @example
## @group
## golombenco (1:4, 2)
## @result{} @{[0 1], [1 0 0], [1 0 1], [1 1 0 0]@}
## golombenco (1:10, 2)
## @result{} @{[0 1], [1 0 0], [1 0 1], [1 1 0 0],
## [1 1 0 1], [1 1 1 0 0], [1 1 1 0 1], [1 1 1 1 0 0],
## [1 1 1 1 0 1], [1 1 1 1 1 0 0]@}
## @end group
## @end example
## @seealso{golombdeco}
## @end deftypefn
function [gcode, Ltot] = golombenco (sig, m)
if (nargin != 2 || m <= 0)
print_usage ();
endif
if (min (sig) < 0)
error ("golombenco: all elements of SIG must be non-negative numbers");
endif
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;
endif
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);
endfor
##
## actual golomb code: sandwich the unary coded quotient,
## and the remainder.
##
gcode{j} = [ones(1, quot(j)) 0 golomb_part];
endfor
Ltot = sum (quot)+Ltot;
endfunction
%!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]})
%% Test input validation
%!error golombenco ()
%!error golombenco (1)
%!error golombenco (1, 2, 3)
%!error golombenco (1, 0)
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