Low-density parity-check codes with simple irregular semi-random parity-check matrix finite-length applications

In this paper, we consider the design of simple irregular low-density parity-check (LDPC) codes with semi-random parity-check matrix for good performance and fast encoding in practical applications with finite-length. We limit the number of degree-two variable nodes to satisfy the semi-random construction and then we optimize a simple irregular structure for the random part of the parity-check matrix with similar technique presented in [Rashidpour et al.]. The procedure is general for any rate and the results are illustrated for finite-length and low rate to high rate applications. The presented code with rate 1/8 is suitable for CDMA application and is slightly better than the best result in [Rashidpour, M et al.] in addition to fast encoding capability. The high rate rode (8/9) is also has a gain about 0.25 dB with respect to one of the best LDPC code used in magnetic recording channel, in addition to fast encoding structure.