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Low-density parity-check (LDPC) codes on symmetric memoryless channels havebeen analyzed using statistical physics by several authors. In this paper,statistical mechanical analysis of LDPC codes is performed for asymmetricmemoryless channels and general Markov channels. It is shown that the saddlepoint equations of the replica symmetric solution for a Markov channel isequivalent to the density evolution of the belief propagation on the factorgraph representing LDPC codes on the Markov channel. The derivation uses themethod of types for Markov chain.

Statistical Mechanical Analysis of Low-Density Parity-Check Codes on General Markov Channel