Communication in the Presence of a State-Aware Adversary

We study communication systems over the state-dependent channels in the presence of a malicious state-aware jamming adversary. The channel has a memoryless state with an underlying distribution. The adversary introduces a jamming signal into the channel. The message and the entire state sequence are known non-causally to both the encoder and the adversary. This state-aware adversary may choose an arbitrary jamming vector depending on the message and the state vector. Taking an arbitrarily varying channel (AVC) approach, we consider two setups, namely, the discrete memoryless Gel'fand-Pinsker AVC and the additive white Gaussian dirty paper (DP) AVC. We determine the randomized coding capacity of both the AVCs under a maximum probability of error criterion. Similar to other randomized coding setups, we show that the capacity is the same even under the average probability of error criterion. Though the adversary can choose an arbitrary vector jamming strategy, we prove that the adversary cannot affect the rate any worse than when it employs a memoryless strategy, which depends only on the instantaneous state. Thus, the AVC capacity characterization is given in terms of the capacity of the worst memoryless channels with state, induced by the adversary employing such memoryless jamming strategies. For the DP-AVC, it is further shown that among memoryless jamming strategies, none impact the communication more than a memoryless Gaussian jamming strategy which completely disregards the knowledge of the state. Thus, the capacity of the DP-AVC equals that of a standard additive white Gaussian noise (AWGN) channel with two independent sources of AWGN, i.e., the channel noise and the jamming noise.