An n-user arbitrarily varying multiple-access channel (AV-MAC) is an information channel that, given n codewords and an adversarial input, outputs a separate word. A channel's capacity is the maximum amount of information that can be sent per bit used over all possible codes. One of the main challenges in information theory is determining what criteria a given channel must have to guarantee that there exists a code such that, with high probability, a given output can be decoded to obtain the original inputs. Any channel that satisfies that criteria is said to have nonzero capacity. A similar, but less restrictive notion is that of partial correction. For a multiple user channel W and real number γ between 0 and 1, we say W is γ partially correctable if it is possible to recover at least a γ fraction of the users' inputs when the adversary acts and recover all users' messages when the adversary does not act. A necessary condition for an AV-MAC to be partially correctable has been found, although the sufficiency of this condition is still an open question. This presentation will focus on sufficiency of this condition after discussing some relevant basic notions in information theory.
