 
Summary: 1
Feedback Capacity of a Class of Symmetric
FiniteState Markov Channels
Nevroz S¸en, Student Member, IEEE, Fady Alajaji, Senior Member , IEEE,
and Serdar Y¨uksel, Member, IEEE
Abstract
We consider the feedback capacity of a class of symmetric finitestate Markov channels. Here,
symmetry (termed "quasisymmetry") is defined as a generalized version of the symmetry defined for
discrete memoryless channels. The symmetry yields the existence of a hidden Markov noise process
that depends on the channel's state process and facilitates the channel description as a function of
input and noise, where the function satisfies a desirable invertibility property. We show that feedback
does not increase capacity for such class of finitestate channels and that both their nonfeedback and
feedback capacities are achieved by an independent and uniformly distributed (i.u.d.) input. As a result,
the channel capacity is explicitly given as a difference of output and noise entropy rates, where the
output is driven by the i.u.d. input.
Index Terms
Channel capacity, channels with memory, finitestate Markov channels, dynamic programming,
feedback capacity.
I. INTRODUCTION AND LITERATURE REVIEW
Although feedback does not increase the capacity of discrete memoryless channels (DMCs)
