Matlab中LDPC编码器和解码器的奇偶校验矩阵

Question

MATLAB provides powerful LDPC encoder and decoder objects in the latest versions. However the parity check matrix H , with dimension (NK) by N , needs to satisfy the following condition:

"The last N−K columns in the parity check matrix H must be an invertible matrix in GF(2) "

Indeed, this condition is not easy to be satisfied for most LDPC codes, although we know that there is at least one (NM) by (NM) invertible sub-block in the parity check matrix H , if H is with a full rank.

I want to know that, if there exists a fast algorithm or a MATLAB function, which can find out an invertible sub-block in H provided H is with a full rank. So that we can use the MATLAB objects and Simulink blocks conveniently.

Answer 1

I tried repermuting the columns of H matrix until it matches the Malab

% Programmer: Taha Valizadeh
% Date: September 2016

%% Column Permutation
% Permute columns of a binary Matrix until the rightmost square matrix is
% invertible over GF(2)

% matrix dimensions:
[~, n] = size(H);

% Initialization
HInvertible = H;
PermutorIndex = 1:n;
flag = true;
counter = 0;

% Initial Report
disp('Creating a ParityCheck matrix which is suitable for MATLAB COMM Tollbox')

% Permute columns
while flag

    % Check if the rightmost square matrix is invertible over GF(2)
    try

        EncoderObject = comm.LDPCEncoder(sparse(HInvertible));  
                                % Check if new matrix works
        fprintf(['ParityCheck Matrix become suitable for Matlab LDPC Encoder ',...
            'after ',num2str(counter),' permutations!\n'])
        flag = false;           % Break the loop

    catch

        % Choose different columns for the rightmost part of matrix
        counter = counter+1;    %Permutation Counter
        PermutorIndex = randperm(n);
        HInvertible = H(:,PermutorIndex);

    end

end