Gallager_girth4.m

% The Program to test the girth 4 of Gallager LDPC codes
% Copyright (C) Yang XIAO, BJTU, July 26, 2007, E-Mail: [e-mail], 
%
% The program analyzes the girth 4 for Gallager LDPC codes.The figures show 
% the parity check matrix H and the girth test matrix O.     
% Theorem in Ref [1]: The H matrix has no gith4, iff the O matrix in Fig.2 has no entry value to
% larger than 1.
% Ref:
% [1] Y. Xiao, M -H Lee,Low complexity MIMO-LDPC CDMA systems over multipath channels, 
% IEICE Transactions on Communications, v E89-B, n 5, May, 2006, p 1713-1717
% [2] J. Fan, Y. Xiao, A method of counting the number of cycles in LDPC codes,
% 8th International Conference on Signal Processing, ICSP 2006,Volume: 3,  
% ISBN: 0-7803-9737-1, Digital Object Identifier: 10.1109/ICOSP.2006.345906
% [3] MOHAMMED ALKHANBASH, Gallager LDPC, Matlab center, File Exchange, 2007
%
% The papers [1] and [2] can be downloaded from Web site of IEICE and IEEE Explore.
%

clear;

% Example: To obtain a H, I revised the program of:MOHAMMED ALKHANBASH, Gallager LDPC, Matlab Center, File Exchange, 2007.  
% The code generated by the program of:MOHAMMED ALKHANBASH is not good, we
% only use it to demo the test procedure for girth 4.
% If you have own H, you need not use the sub-program.
%
n=1200                         %Code length
c=n/2                          %Length of parity check bits 
wc=3                           %wc: the number of ones in each columns
wr=(n.*wc)./c                  %wr:the number of ones in each row
h=zeros(c,n);                   %generate the empty matrix and start 
                                %assigning the 1s 
%Step 1:LDPC Code Generatio
    onesvector=ones(1,wr);
    start=1;
    finish=wr;   

    for ii = 1:c./wc

       h(ii,start:finish)=1;        
       start=start+wr;              
       finish=(ii.*wr)+wr;          
    end

  for i=1:wc-1
    r=1;

       for ii=1:n
       col_index = (round(rand(1) * (n-1) ))+1;
       randomCol=h(1:fix(c/wc),col_index);
            
       h((i*fix(c/wc))+1   :  ((i*(c/wc))+1  +  fix(c/wc)-1),ii )=randomCol;
               
       end
       r=r+1;
  end
  
%%%%%%% Girth4 Test %%%%%
% Here, we only concern whether a parity matrix H has girth4, instead of
% the number of girth4. If you need know the nember of girth 4, please
% refer Ref. [2].
% get the number of H
rows=size(h,1);
cols=size(h,2);

% We can test girth 4 by using the matrix O, see [1].

O=h*h';   
for i=1:rows
    O(i,i)=0;
end
for i=1:rows
girth(i)=max(O(i,:));
end
girth4=max(girth);

if girth4<2 
  fprintf('No girth 4')
else
   fprintf('The H matrix has girth 4\n')  % Provde the test result.
end    
% Display the matrice H and O
% If H matrix has no gith4, the O matrix in Fig.2 has no entry value to
% larger than 1.
figure(1)
mesh(h)
figure(2)
mesh(O)
fprintf('Please see your H matrix in Fig. 1, and the O matrix in Fig.2')