Symmetric Characterization of Finite State Markov Channels

In this paper the symmetry property for discrete memoryless channels is generalized to finite state Markov channels. We show that for symmetric Markov channels the noise process can be characterized as a hidden Markov process, and the capacity of channel is related to the entropy rate of this process. These results elaborate the characterization of symmetry for Markov channels in previous narrations and extend the capacity formulae for symmetric discrete memoryless channel to symmetric Markov channels. Using recent formulation of entropy rate of hidden Markov process, this capacity formula is shown to be equivalent to the previous formulations which have been obtained for special cases of symmetric Markov channels