Capacity-Maximizing Input Symbol Selection for Discrete Memoryless Channels

TL;DR

This paper addresses the problem of selecting input symbols for discrete memoryless channels to maximize capacity, proposing a clustering-based algorithm guided by a theoretical capacity loss bound, with numerical validation.

Contribution

It introduces a novel clustering-based input symbol selection algorithm for DMCs, leveraging a new capacity loss bound to guide the selection process.

Findings

The proposed algorithm effectively maximizes channel capacity with constrained input symbols.

Theoretical bounds provide reliable guidance for symbol subset selection.

Numerical experiments demonstrate the algorithm's practical performance.

Abstract

Motivated by communication systems with constrained complexity, we consider the problem of input symbol selection for discrete memoryless channels (DMCs). Given a DMC, the goal is to find a subset of its input alphabet, so that the optimal input distribution that is only supported on these symbols maximizes the capacity among all other subsets of the same size (or smaller). We observe that the resulting optimization problem is non-concave and non-submodular, and so generic methods for such cases do not have theoretical guarantees. We derive an analytical upper bound on the capacity loss when selecting a subset of input symbols based only on the properties of the transition matrix of the channel. We propose a selection algorithm that is based on input-symbols clustering, and an appropriate choice of representatives for each cluster, which uses the theoretical bound as a surrogate objective function. We provide numerical experiments to support the findings.