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.

翻译：本文提出了一类新型编码，称为加权奇偶校验码，其中每个奇偶校验比特具有一个权重，指示其为1的可能性（而非将每个奇偶校验比特固定为0）。该编码适用于多种场景，例如非对称信道、具有状态和/或成本约束的信道，以及Wyner-Ziv问题，并且可证明能够达到信道容量。对于有状态信道（Gelfand-Pinsker）场景，所提出的编码方案与嵌套线性码相比具有两个优势：首先，它能达到任何有状态信道（例如非对称信道）的容量；其次，仿真结果表明，与嵌套线性码相比，该编码实现了更低的误码率。我们还讨论了一种稀疏构造方法，其中可应用置信传播算法来提高编码效率。