# Computing the channel capacity of a communication system affected by uncertain transition probabilities

## TL;DR

This paper develops a first-order optimization algorithm to compute the capacity of uncertain discrete memoryless channels efficiently, especially for large-scale problems, by transforming the max-min problem into a convex optimization problem.

## Contribution

It introduces an $ ext{O}(1/T)$ first-order method for solving the robust channel capacity problem under uncertainty, improving scalability over interior point methods.

## Key findings

- Algorithm effectively computes channel capacity under uncertainty.
- Applicable to large-scale problems where traditional methods are impractical.
- Transforms max-min problem into a convex optimization problem.

## Abstract

We study the problem of computing the capacity of a discrete memoryless channel under uncertainty affecting the channel law matrix, and possibly with a constraint on the average cost of the input distribution. The problem has been formulated in the literature as a max-min problem. We use the robust optimization methodology to convert the max-min problem to a standard convex optimization problem. For small-sized problems, and for many types of uncertainty, such a problem can be solved in principle using interior point methods (IPM). However, for large-scale problems, IPM are not practical. Here, we suggest an $\mathcal{O}(1/T)$ first-order algorithm based on Nemirovski (2004) which is applied directly to the max-min problem.