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

翻译：我们认为,在两个传输端的确定性对立多存取频道(MAC)上,我们考虑在两个传输端的确定性对立多存取频道(MAC)上进行零度通信。在这项工作中,由于两个传输端的任意确定性随机对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对立式对式对式对立式对立式对立式对立式对立式对式对立式对式对式对式对式对立式。。。。。。。上对立式对立式对立式对立式对立式对立式对立式对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面对面