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 channel with state (Gelfand-Pinsker) setting, the proposed coding scheme has two advantages. 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 codes. We also discuss a sparse construction where the belief propagation algorithm can be applied to improve the coding efficiency.