A Randomized Algorithm for the Capacity of Finite-State Channels

Abstract

Inspired by ideas from the field of stochastic approximation, we propose a ran- domized algorithm to compute the capacity of a finite-state channel with a Markovian input. When the mutual information rate of the channel is concave with respect to the chosen parameterization, the proposed algorithm proves to be convergent to the ca- pacity of the channel almost surely with the derived convergence rate. We also discuss the convergence behavior of the algorithm without the concavity assumption.