girth6_shifter.m

Flexible construction of girth-six QC-LDPC Codes

% This program constructs girth 6 quasi-cyclic LDPC codes given
% row weight(k),column-weight (j) and size of each sub-matrix (m). The
% program  calculates the shift value of each sub-matrix stored in an array called `shift'. 
%The shift values are then used to construct a QC-LPDC code H. The first row sub-matrices are
% not shifted. Hence they remain as identity sub-matrices. 
% The obtained code is stored in matrix H.
% Author : Dr. Gabofetswe Alafang Malema,University of Botswana  
% Department of Computer science. e-mail: [e-mail]

clear
pack
clear
pack

j=3; % variable column-weight. change it to your desired column weight.
k=8; % row-weight is also variable.
m=10; % size of each sub-matrix is also variable.
p=[1:m];
M=j*m; % total number of rows.
shift=zeros(j,k); % stores shift values for each sub-matrix.
rows = struct('connect',0,'counter',0,'con',0); % structure used for storing connections.
shifter = struct('mem',0);
emptyset = [];
for y = 1:M       % connections and number of connections for rows and columns are initialized.
    rows(y).counter = 0;
    rows(y).con = intersect(emptyset,rows(y).con);
    rows(y).connect = intersect(emptyset,rows(y).connect);
    
end
for y =1:j
    shifter(y).mem =[];
    gp(y).mem=[(y-1)*m+1:y*m];
end

%This for loop calculates sub-matrix shift values. The calculation avoids
% shift values resulting in four-cycles. Shifts values are not repeated in
% the same row-group or column-group and two connections in the same groups 
% must not have the same difference.
for a=1:k
    for b=2:j
        if a==1
            shift(b,a)=ceil(rand*m);
            shifter(b).mem = union(shifter(b).mem,shift(b,a));
        else
            if b==2
                x1=setxor(shifter(b).mem,p);
                r=ceil(rand*(length(x1)));
                shift(b,a)=x1(r);
                shifter(b).mem=union(shifter(b).mem,x1(r));
            else
                done =0; x1=setxor(shifter(b).mem,p);
                while done==0
                    if isempty(x1)==1
                        display('Could not find code!! Try again or increase size of group.');
                        break;
                    end
                    r=ceil(rand*length(x1));
                    x=x1(r);
                    reject=0;
                    for d=b:-1:3
                        for e=a-1:-1:1
                            d1=x-shift(b,e);
                            d1=mod(d1,m);
                            d2=shift(d-1,a)-shift(d-1,e);
                            d2=mod(d2,m);
                            if d1==d2
                                reject=1;
                            end
                        end
                    end
                    if reject==0   %isempty(intersect(d11,d22))==1
                        shift(b,a)=x;
                        shifter(b).mem=union(shifter(b).mem,x);
                        done =1;
                        break;
                    else
                        x1=setxor(x1,x);
                    end
                end % while loop
            end % if b==2
        end % if a == 1
    end % for b=2:j
end % for a=1:k

% use the shift values to create connections in sub-matrices.
for i =1:k
    for y=1:j
        g(y).mem =circshift(gp(y).mem,[1 -shift(y,i)]);
    end
    for b=1:m
        for y=2:j
            rows(b).connect(i,y-1)= g(y).mem(b);
        end
    end
end
    
% use the row connections to form a matrix code.  
counter = 1; 
 H = zeros(M,5);
for i = 1:k
     for z = 1:m
         H(z,counter)=1;
         for y=1:j-1
             x=rows(z).connect(i,y);
             H(x,counter)=1;
         end
         counter = counter + 1;
     end
 end