Parity check matrix of LDPC encoder and decoder in Matlab

MATLAB provides powerful LDPC encoder and decoder objects in the latest versions. However the parity check matrix H, with dimension (N-K) 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 (N-M) by (N-M) 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.

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