This program presents an approach [1] for constructing the short length of LDPC codes with girth 8. First, we design 3 submatrices with different shifting functions given by our schemes, then combine them into a matrix according to our approach, finally, expand the matrix into a desired parity-check matrix using identity matrices and cyclic shift matrices of the identity matrices.

The simulation results in AWGN channels show that the codes which can be obtained by the generator matrix derived from this check matrix for encoding the random information bits are as good as random LDPC codes [1].

Ref:
[1] J. Fan, Y. Xiao, “A design of LDPC codes with large girth based on the sub-matrix shifting”, IET International Conference on Wireless Mobile and Multimedia Networks Proceedings (ICWMMN 2006), (CP525), p. 295, Hangzhou, China, 6-9 Nov. 2006 , ISBN: 0 86341 644 6
[2] J. Fan, Y. Xiao, A method of counting the number of cycles in LDPC codes, 8th International Conference on Signal Processing, ICSP 2006,Volume: 3, ISBN: 0-7803-9737-1, Digital