Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / communications-1.1.1 / golombenco.m

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+## 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]})
+%!