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golombenco.m

## 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 2 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),{,,})
%! assert(golombenco(3:5,3),{ , ,})
%! 

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