Zero-Error Communication over Adversarial MACs

We consider zero-error communication over a two-transmitter deterministic adversarial multiple access channel (MAC) governed by an adversary who has to the transmissions of both senders (hence called omniscient ) and aims maliciously corrupt communication. None encoders, jammer decoder is allowed randomize using private or public randomness. This enforces combinatorial nature problem. Our model covers large family channels studied in literature, including all discrete memoryless noisy noiseless MACs. In this work, given arbitrary omniscient MAC, we characterize when capacity region 1) nonempty interior (in particular, two-dimensional); 2) consists two line segments empty interior); 3) one segment one-dimensional); 4) only contains (0, 0) zero-dimensional). extends recent result Wang, Budkuley, Bogdanov Jaggi (2019) from point-to-point setting setting. Indeed, our converse arguments build upon their generalized Plotkin bound involve delicate case analysis. One technical challenges take care “joint confusability” “marginal confusability”. treatment marginal confusability does xmlns:xlink="http://www.w3.org/1999/xlink">not follow results Wang et al. achievability random coding with expurgation.