Nonbinary multi-parallel-concatenated single-parity-check (NB-MPCSPC) codes over partial-response channels

In this paper, we propose a high-rate nonbinary multi-parallel-concatenated single-parity-check (NB-MPCSPC) code as a low-complexity coding scheme for data storage channels. The proposed scheme is composed of parallel branches of nonbinary SPC codes over a Galois Field (GF) and can be flexibly designed to achieve a wide range of code rates and codeword lengths. The encoding can be directly implemented based on the parity-check matrix; while the decoding is simplified by using the first-order MacLaurin Series to approximate the check-node operation. Compared with its binary counterpart, the proposed nonbinary coding scheme significantly improves bit-error-rate (BER) performance in the error-floor region. Simulation results show that a noticeable performance gain is obtained over conventional binary low-density parity-check (LDPC) codes when used in turbo equalization for partial-response channels.