Concavity of Mutual Information Rate for Input-Restricted Finite-State Memoryless Channels at High SNR

TL;DR

This paper proves that the mutual information rate of input-restricted finite-state memoryless channels is concave at high SNR, facilitating better numerical capacity estimation.

Contribution

It establishes the concavity of mutual information rate with respect to input Markov process parameters at high SNR for these channels.

Findings

Mutual information rate is concave at high SNR.

Concavity enables efficient numerical capacity approximation.

Analysis of entropy rate of output hidden Markov chains.

Abstract

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.