Feedback capacity of a class of symmetric finite-state Markov channels

In this paper we consider the feedback capacity of a class of symmetric finite-state Markov channels. For this type of channels, symmetry is a generalized version of the symmetry defined for discrete memoryless channels. We show that feedback does not increase capacity for such class of finite-state channels. We indeed demonstrate that for such channels, both non-feedback and feedback capacities are achieved by a uniform i.i.d. input distribution.