A design of LDPC codes with large girth based on the sub-matrix shifting

In this paper, we present an approach for constructing 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 these 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.