On Capacity Computation for the Two-User Binary Multiple-Access Channel

TL;DR

This paper investigates the challenging problem of computing the capacity boundary for the two-user binary multiple-access channel, providing conditions under which the optimization simplifies to a one-dimensional pseudoconcave problem.

Contribution

It introduces a method to identify when the capacity boundary can be efficiently computed for certain channel classes by reducing the problem to a simpler optimization.

Findings

Optimal solutions lie on the boundary or have at most one interior stationary point.

The problem reduces to a pseudoconcave one-dimensional optimization.

Conditions depend on an ordering property of the channel matrix.

Abstract

This paper deals with the problem of computing the boundary of the capacity region for the memoryless two-user binary-input binary-output multiple-access channel ((2,2;2)-MAC), or equivalently, the computation of input probability distributions maximizing weighted sum-rate. This is equivalent to solving a difficult nonconvex optimization problem. For a restricted class of (2,2;2)-MACs and weight vectors, it is shown that, depending on an ordering property of the channel matrix, the optimal solution is located on the boundary, or the objective function has at most one stationary point in the interior of the domain. For this, the problem is reduced to a pseudoconcave one-dimensional optimization and the single-user problem.