We propose a modified algorithm for decoding of low-density parity check codes over finite-state binary Markov channels. The hidden Markov model representing the channel is incorporated into the bipartite graph of the low-density parity check code, and the message passing algorithm is modified accordingly. This approach clearly outperforms systems in which the channel statistics are not exploited in the decoding, allowing reliable communication at rates which are above the capacity of a memoryless channel with the same stationary bit error probability as the Markov channel. Moreover, we introduce a joint estimation/decoding method that allows the estimation of the parameters of the channel when they are not known a priori.
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