Communication in the Presence of a State-Aware Adversary

TL;DR

This paper characterizes the capacity of state-dependent channels with a malicious, state-aware jammer, showing that the worst-case jamming strategy is memoryless and that the capacity can be explicitly determined for Gaussian channels.

Contribution

It provides a capacity characterization for state-dependent AVCs with a malicious adversary, demonstrating the adversary's optimal strategies and their impact on capacity.

Findings

Capacity is unaffected by the adversary's non-causal knowledge of the state.

The worst-case jamming strategy is memoryless, depending only on the current state.

For Gaussian channels, the capacity equals that of a standard AWGN channel with additive noise.

Abstract

We study communication systems over 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 state sequence is known non-causally to both the encoder and the adversary. Taking an Arbitrarily Varying Channel (AVC) approach, we consider two setups, namely, the discrete memoryless Gel'fand-Pinsker (GP) 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. Even with non-causal knowledge of the state, we prove that the state-aware 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 AWGN channel with two independent sources of additive white Gaussian noise, i.e., the channel noise and the jamming noise.