Concavity of the mutual information rate for input-restricted memoryless channels at high SNR

We consider a finite-state memoryless channel with i.i.d. channel state and the input Markov process supported on a mixing finite-type constraint. We discuss the asymptotic behavior of entropy rate of the output hidden Markov chain and deduce that the mutual information rate of such a channel is concave with respect to the parameters of the input Markov processes at high signal-to-noise ratio. In principle, the concavity result enables good numerical approximation of the maximum mutual information rate and capacity of such a channel. 1 Channel Model In this paper, we show that for certain input-restricted finite-state memoryless channels, the mutual information rate, at high SNR, is effectively a concave function of Markov input processes of a given order. While not directly addressed here, the goal is to help estimate the maximum of this function and ultimately the capacity of such channels (see, for example, the algorithm of Vontobel, et. al. [11]). Our approach depends heavily on results regarding asymptotics and smoothness of en