In this paper, we propose the construction of quasi-cyclic (QC) LDPC codes based on the modified progressive edge-growth (PEG) algorithm to achieve the maximum local girth. Although the previously designed QC-LDPC codes based on the PEG algorithm has more flexible code rates than the conventional QC-LDPC code, in the design process, multiple choices of the edges may be chosen. In the proposed algorithm, we aim to maximize the girth property by choosing the suitable edges and thus improve the error correcting performance. Simulation results show that the QC-LDPC codes constructed from the proposed method give higher proportion of high local girths than other methods, particularly, at high code rates. In addition, the proposed codes offer superior bit error rate and block error rate performances to the previous PEG-QC codes over the additive white Gaussian noise (AWGN) channel.

Low-density parity-check (LDPC) codes are typically designed to avoid the length-4 cycles to ensure acceptable levels of performance. However, the turbo equalization, which relies on an interaction between an inner code such as an LDPC code and a soft-output Viterbi algorithm (SOVA) detector, exhibits a performance degradation due to the pseudo cycles. In this paper, we propose an interleaved modified array code (IMAC) that can reduce the number of pseudo cycles, hence, improving the gains from the iterative processing technique. The modification is made on the existing array-based LDPC codes named modified array codes (MAC) by introducing an additional interleaving matrix to the parity-check matrix. Simulation results on the perpendicular magnetic recording channels (PMRC) demonstrate that the IMAC outperforms both the MAC and the previously proposed random interleave array (RIA) codes for the partial-response targets under consideration. In addition, a subblock-based encoder design is proposed to reduce the encoding complexity of the IMAC and when compared with the RIA code, the IMAC exhibits a lower encoding complexity, and still maintains a comparable level of the decoding complexity.