Add a useful package (from Source forge) for octave

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

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+## Copyright (C) 2007 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} {}  reedmullergen (@var{R},@var{M})
+##
+## Definition type construction of Reed Muller code,
+## of order @var{R}, length @math{2^M}. This function
+## returns the generator matrix for the said order RM code.
+## 
+## RM(r,m) codes are characterized by codewords,
+## @code{sum ( (m,0) + (m,1) + @dots{} + (m,r)}.
+## Each of the codeword is got through spanning the
+## space, using the finite set of m-basis codewords.
+## Each codeword is @math{2^M} elements long.
+## see: Lin & Costello, "Error Control Coding", 2nd Ed.
+##
+## Faster code constructions (also easier) exist, but since 
+## finding permutation order of the basis vectors, is important, we 
+## stick with the standard definitions. To use decoder
+## function reedmullerdec,  you need to use this specific
+## generator function.
+##
+## @example
+## @group
+## G=reedmullergen(2,4);
+## @end group
+## @end example
+##
+## @end deftypefn
+## @seealso{reedmullerdec,reedmullerenc}
+function G=reedmullergen(R,M)
+    if ( nargin < 2 )
+       print_usage();
+    end
+
+    G=ones(1,2^M);
+    if ( R == 0 )
+        return;
+    end
+    
+    a=[0];
+    b=[1];
+    V=[];
+    for idx=1:M;
+        row=repmat([a,b],[1,2^(M-idx)]);
+        V(idx,:)=row;
+        a=[a,a];
+        b=[b,b];
+    end
+    
+    G=[G; V];
+
+    if ( R == 1 )
+        return
+    else
+        r=2;
+        while r <= R
+            p=nchoosek(1:M,r);
+            prod=V(p(:,1),:).*V(p(:,2),:);
+            for idx=3:r
+                prod=prod.*V(p(:,idx),:);
+            end
+            G=[G; prod];
+            r=r+1;
+        end
+    end
+    return
+end