Dirty Paper Arbitrarily Varying Channel with a State-Aware Adversary

TL;DR

This paper investigates the capacity limits of writing on a dirty paper in the presence of an adversary who can arbitrarily jam the channel, revealing that the adversary ignores the state information when choosing its jamming strategy.

Contribution

It characterizes the randomized coding capacity of a Gaussian AVC with state known to encoder and adversary but not decoder, highlighting the adversary's optimal jamming behavior.

Findings

Adversary disregards state knowledge in jamming strategy.

Capacity is characterized under maximal error probability.

Optimal jamming input is independent of the state.

Abstract

In this paper, we take an arbitrarily varying channel (AVC) approach to examine the problem of writing on a dirty paper in the presence of an adversary. We consider an additive white Gaussian noise (AWGN) channel with an additive white Gaussian state, where the state is known non-causally to the encoder and the adversary, but not the decoder. We determine the randomized coding capacity of this AVC under the maximal probability of error criterion. Interestingly, it is shown that the jamming adversary disregards the state knowledge to choose a white Gaussian channel input which is independent of the state.