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

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 $\mathrm{\Omega }$ called its symmetrizability. It is shown that for every $L\le \mathrm{\Omega }$, $C_L$ has an empty interior, and for every $L\ge (\mathrm{\Omega }+1{)}^2$, $C_L$ 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.