How to generating LDPC parity-check matrices with arbitrary sizes?

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]?  

How to generating LDPC parity-check matrices with arbitrary sizes?

Answer 1

[David Ding]

Hi Hamid,

I believe you might find the following link useful:

http://mathforum.org/kb/message.jspa?messageID=9818971

Essentially, you just need to do a bit of pre-processing on the parity check matrix in permuting its columns, such that the last (n-k) columns of the new H is always invertible in F_2. To do this, as the author in the link suggested, you may use:

% Permute H to obtain a systematic code
% This is always possible if H has full rank and if infobits_loc is
% correctly defined

paritybits_loc = setdiff(1:size(H,2),infobits_loc);
H2 = H(:,[infobits_loc paritybits_loc]);

Hope this helps.

David

[Cheng Guo]

Sorry, the link that you gave here is not accesssible. Can you give me a new one? I need to know how to build up customized LPDC matrix which has user designed input length and output length.

I'm really appreciate to any help and time of you.

[Zeyad Qasem]

Hi Cheng, Have you got the answer of this question?, I'm also stuck in that same issue.

[han xiangqun]

Generating LDPC parity-check matrices with arbitrary sizes (narkive.com)