I want to use comm.LDPCEncoder/comm.LDPCDecoder and i know to use this encoder decoder in Matlab the H matrices should be Systematic (support Systematic codes only) otherwise i will receive this error.

"the last (N-K) columns of the parity-check matrix must be invertible in GF(2)."

I know two methods from MATLAB that will generate parity-check matrices:

H = dvbs2ldpc(r)

h = hammgen(m)

However, these methods are restricted to a certain ratio between rows and columns. I tried some other third-party scripts to generate the matrix, but some of them don't seem to return a valid matrix, since "comm.LDPCDecoder" will fail with the same error.

I used some predefined H matrices of Mackay, but no way.

lent of my code-word is not fix it's about 1000 to 3000 it depend to the situation of my simulation(for example code-word length is equal to 1536 or another case 2048), that's why i should create a spars matrix then use it.

Now how to generate the LDPC parity-check matrices with arbitrary sizes[depend to length of my code-word]?