A Randomized Approach to the Capacity of Finite-State Channels

TL;DR

This paper introduces a randomized algorithm inspired by stochastic approximation to estimate the capacity of finite-state channels with Markovian inputs, proving convergence under certain conditions.

Contribution

It presents a novel stochastic approximation-based method for computing channel capacity and analyzes its convergence properties.

Findings

Algorithm converges almost surely when mutual information is concave.

Derived explicit convergence rate of the proposed algorithm.

Discussed convergence behavior without the concavity assumption.

Abstract

Inspired by the ideas from the field of stochastic approximation, we propose a randomized 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, we show that the proposed algorithm will almost surely converge to the capacity of the channel and derive the rate of convergence. We also discuss the convergence behavior of the algorithm without the concavity assumption.