Doubly multistage decoding of low-density parity-check codes over ℤ2m.

A doubly multistage decoder (DMD) for low-density parity-check codes over ℤ2m, m > 1, which fuses the multistage decoding approaches of Armand et al. and Varnica et al., is proposed. Two variants of the DMD are considered. The first (respectively, second) performs belief-propagation (BP) [respectively, offset min-sum (OMS)] decoding in each decoding stage and is referred to as DMD -- BP (respectively, DMD -- OMS). For the moderate-length codes considered in this study, the computer simulations show the DMD -- BP (respectively, DMD -- OMS) achieving coding gains of up to 0.43 dB (respectively, 0.67 dB) over standard BP decoding at a bit error rate of 10-6 on an additive-white-Gaussian-noise channel, while requiring significantly less computational power. Remarkably, DMD -- OMS outperforms DMD -- BP, yet has lower computational complexity than DMD -- BP. Snapshots of the log-likelihood ratio densities of the decoded bits midway through the decoding process explain the superiority of the DMD over standard BP decoding. [ABSTRACT FROM AUTHOR]