Weighted Parity-Check Codes for Channels with State and Asymmetric Channels

TL;DR

This paper introduces weighted parity-check codes that adapt to channel asymmetries and states, achieving capacity and lower error rates, with efficient sparse constructions for practical decoding.

Contribution

It proposes a novel class of weighted parity-check codes that outperform nested linear codes in capacity achievement and error rate, applicable to various complex channels.

Findings

Achieves capacity for channels with state and asymmetry

Reduces error rates compared to nested linear codes

Enables efficient decoding via sparse constructions

Abstract

In this paper, we introduce a new class of codes, called weighted parity-check codes, where each parity-check bit has a weight that indicates its likelihood to be one (instead of fixing each parity-check bit to be zero). It is applicable to a wide range of settings, e.g. asymmetric channels, channels with state and/or cost constraints, and the Wyner-Ziv problem, and can provably achieve the capacity. For the channels with state (Gelfand-Pinsker) setting, the proposed coding scheme has two advantages compared to the nested linear code. First, it achieves the capacity of any channel with state (e.g. asymmetric channels). Second, simulation results show that the proposed code achieves a smaller error rate compared to the nested linear code. We also discuss a sparse construction where the belief propagation algorithm can be applied to improve the coding efficiency.