Multiple Access Channels with Byzantine Users

Communication over a three-user multiple access channel (MAC) is studied when any one of the users may behave adversarially. The capacity region is characterized for randomized codes (where each user shares an independent secret key with the receiver). The capacity region for deterministic codes is also studied. Necessary conditions including a new non-symmetrizability condition is obtained for this capacity region to be non-trivial. It is shown that when none of the users are symmetrizable, the randomized coding capacity region is also achievable with deterministic codes. This is analogous to the result of Ahlswede and Cai (1991) for arbitrarily varying MAC.