Performance of Multistage Universal Decoder for Given Linear Codes over Additive Noise Channels

Aleksey Kuvshinov, Anna A. Fominykh, Fedor I. Ivanov

Tomohiko Uyematsu, Fumio Kanaya

We propose a multilevel coding and multistage decod-ing scheme which is universal for a class of additive noise channels. Then, for a given pair of binary linear codes, we show an upper bound of the decoding er-ror probability. Further, we clarify the condition that the proposed coding and decoding scheme achieves the capacity of the channel and that the decoding error probability vanishes exponentially with code length. 1.

Paulo Ricardo Branco da Silva, Danilo Silva

Lattice codes are elegant and powerful structures that not only achieve the capacity of the additive white Gaussian noise (AWGN) channel but are also a key ingredient to many multiterminal schemes that exploit linearity properties. However, constructing lattice codes that can realize these benefits with low complexity is still a challenging problem. In this paper, efficient encoding and decoding algorithms are proposed for multilevel binary low-density parity-check (LDPC) lattices constructed via Construction D' whose complexity is linear in the total number of coded bits. Moreover, a generalization of Construction D' is proposed, which relaxes some of the nesting constraints on the parity-check matrices of the component codes, leading to a simpler and improved design. Based on this construction, low-complexity multilevel LDPC lattices are designed whose performance under multistage decoding is comparable to that of polar lattices and close to that of low-density lattice codes on the power-unconstrained AWGN channel.

Eirik Rosnes

Ilya I. Dumer

Haifeng Yuan, M.A. Armand

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.