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

摘要

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 $LleqOmega$, $C_{L}$ has an empty interior, and for every $Lgeq(Omega+1)^{2}$, $C_{L}$ 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.