Improved Min-Sum Decoding for 2-D Intersymbol Interference Channels

In this paper, 2-D normalized min-sum (NMS) algorithm and offset min-sum (OMS) algorithm are proposed for efficient decoding of low-density parity-check (LDPC) codes in 2-D intersymbol interference (ISI) ultra-high density magnetic recording channels, such as bit-patterned magnetic recording and 2-D magnetic recording, where a reduced-complexity 2-D detector based on the iterative row-column soft detection feedback with Gaussian approximation detector is employed instead of the full 2-D Bahl-Cocke-Jelinek-Raviv (BCJR) detector. The normalization and offset factors of the 2-D NMS and 2-D-OMS, are optimized based on the extended density evolution for LDPC coded 2-D ISI channel, respectively. Simulation results show the performance loss caused by the reduced-complexity LDPC decoder can be almost fully recovered by the proposed approaches, while retaining the benefit of low complexity in decoder compared with the belief propagation (BP) decoding. Furthermore, both the NMS and OMS exhibit a lower error floor than that of BP decoding in high signal-to-noise ratio region.