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[CreaPhase.git] / octave_packages / communications-1.1.1 / systematize.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} {}  systematize (@var{G})
+## 
+## Given @var{G}, extract P partiy check matrix. Assume row-operations in GF(2).
+## @var{G} is of size KxN, when decomposed through row-operations into a @var{I} of size KxK
+## identity matrix, and a parity check matrix @var{P} of size Kx(N-K).
+## 
+## Most arbitrary code with a given generator matrix @var{G}, can be converted into its
+## systematic form using this function.
+##
+## This function returns 2 values, first is default being @var{Gx} the systematic version of
+## the @var{G} matrix, and then the parity check matrix @var{P}.
+##
+## @example
+## @group
+##   G=[1 1 1 1; 1 1 0 1; 1 0 0 1];
+##   [Gx,P]=systematize(G);
+##    
+##   Gx = [1 0 0 1; 0 1 0 0; 0 0 1 0];
+##   P = [1 0 0];
+## @end group
+## @end example
+##
+## @end deftypefn
+## @seealso{bchpoly,biterr}
+function [G,P]=systematize(G)
+    if ( nargin < 1 )
+         print_usage();
+    end
+    
+    [K,N]=size(G);
+
+    if ( K >= N )
+         error('G matrix must be ordered as KxN, with K < N');
+    end
+    
+    %
+    % gauss-jordan echelon formation,
+    % and then back-operations to get I of size KxK
+    % remaining is the P matrix.
+    % 
+    
+    for row=1:K
+    
+    %
+    %pick a pivot for this row, by finding the
+    %first of remaining rows that have non-zero element
+    %in the pivot.
+    %
+    
+    found_pivot=0;
+    if ( G(row,row) > 0 )
+       found_pivot=1;
+    else
+     %
+     % next step of Gauss-Jordan, you need to
+     % re-sort the remaining rows, such that their
+     % pivot element is non-zero.
+     %    
+     for idx=row+1:K
+        if ( G(idx,row) > 0 )            
+            tmp=G(row,:);
+            G(row,:)=G(idx,:);
+            G(idx,:)=tmp;
+            found_pivot=1;
+            break;
+        end
+     end
+    end
+  
+    %
+    %some linearly dependent problems:
+    %
+    if ( ~found_pivot )
+        error('cannot systematize matrix G');
+        return
+    end
+
+    %
+    % Gauss-Jordan method:
+    % pick pivot element, then remove it
+    % from the rest of the rows.
+    %    
+    for idx=row+1:K
+        if( G(idx,row) > 0 )
+            G(idx,:)=mod(G(idx,:)+G(row,:),2);
+        end
+    end 
+    
+    end
+      
+    %
+    % Now work-backward.       
+    %
+    for row=K:-1:2
+        for idx=row-1:-1:1
+            if( G(idx,row) > 0 )
+                G(idx,:)=mod(G(idx,:)+G(row,:),2);
+            end
+        end
+    end
+    
+    %I=G(:,1:K);
+    P=G(:,K+1:end);
+    return;
+end