On the Deterministic Code Capacity Region of an Arbitrarily Varying Multiple-Access Channel Under List Decoding

TL;DR

This paper characterizes the deterministic list decoding capacity region of arbitrarily varying multiple-access channels, revealing how symmetrizability influences the capacity and establishing conditions under which the capacity region is nonempty or matches the random code capacity.

Contribution

It introduces the symmetrizability parameter for AVMACs and determines the list decoding capacity region based on this parameter, extending known results from point-to-point channels.

Findings

For L ≤ Ω, the capacity region has an empty interior.

For L ≥ (Ω+1)^2, the list decoding capacity equals the random code capacity.

Symmetrizability is always finite for binary AVMACs with nondegenerate capacity.

Abstract

We study the capacity region $C_L$ of an arbitrarily varying multiple-access channel (AVMAC) for deterministic codes with decoding into a list of a fixed size $L$ and for the average error probability criterion. Motivated by known results in the study of fixed size list decoding for a point-to-point arbitrarily varying channel, we define for every AVMAC whose capacity region for random codes has a nonempty interior, a nonnegative integer $\Omega$ called its symmetrizability. It is shown that for every $L \leq \Omega$, $C_L$ has an empty interior, and for every $L \geq (\Omega+1)^2$, $C_L$ equals the nondegenerate capacity region of the AVMAC for random codes with a known single-letter characterization. For a binary AVMAC with a nondegenerate random code capacity region, it is shown that the symmetrizability is always finite.