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

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