The arbitrarily varying channel when the jammer knows the channel input

The arbitrarily varying channel can be modeled as communication in the presence of a jammer. In this paper we propose a new model: a jammer who knows the channel input, and where the transmitter and receiver share a secret random key. Shared randomness differentiates this scenario from the case where the jammer knows the message. For sufficiently large key rate, we determine the capacity of this channel (which may be strictly smaller than the case where the jammer knows only the message). We also provide an upper bound on the minimum key rate required to achieve capacity. We prove that additionally revealing the message to the jammer does not change the capacity, provided the key rate is sufficiently large. This new capacity result differs from existing results for the AVC, and in fact coincides with a well-known upper bound on the deterministic coding capacity of the AVC with maximum error. Without secret keys, our problem degenerates to deterministic coding for the AVC with maximum probability of error, a well-known hard problem. Our results demonstrate that knowledge of the channel input is better than knowledge of the message for the jammer.