  Low-density parity-check (LDPC) codes on symmetric memoryless channels have
been analyzed using statistical physics by several authors. In this paper,
statistical mechanical analysis of LDPC codes is performed for asymmetric
memoryless channels and general Markov channels. It is shown that the saddle
point equations of the replica symmetric solution for a Markov channel is
equivalent to the density evolution of the belief propagation on the factor
graph representing LDPC codes on the Markov channel. The derivation uses the
method of types for Markov chain.
