# The Capacity Region of the Arbitrarily Varying MAC: With and Without Constraints

## TL;DR

This paper characterizes the capacity regions of arbitrarily varying multiple access channels (AVMAC) with and without constraints, resolving open problems and revealing discontinuities in deterministic capacity boundaries.

## Contribution

It provides a complete characterization of the AVMAC capacity regions under input and state constraints, including the missing cases in prior work.

## Key findings

- Deterministic capacity boundary is discontinuous with input constraints.
- Complete characterization of AVMAC capacity regions with constraints.
- Resolved two open cases in the AVMAC capacity problem.

## Abstract

We determine both the random code capacity region and the deterministic code capacity region of the arbitrarily varying multiple access channel (AVMAC) under input and state constraints. As in the single user case, the boundary of the deterministic code capacity region is a discontinuous function of the input constraint. For the AVMAC without constraints, the characterization due to Ahlswede and Cai is complete except for two cases, pointed out in the literature as an open problem. The missing piece is obtained as a special case of our results.