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

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.