Communication over an Arbitrarily Varying Channel under a State-Myopic Encoder

TL;DR

This paper investigates the capacity of a communication system over an arbitrarily varying channel with a state known non-causally to the encoder through a noisy observation, providing capacity characterizations under different randomization scenarios.

Contribution

It characterizes the capacity of a state-dependent AVC with a noisy state observation at the encoder, including cases with shared randomness and encoder-only randomization.

Findings

Capacity with shared randomness is characterized.

Capacity remains unchanged with encoder-only randomization when positive.

Special cases of the model are also analyzed.

Abstract

We study the problem of communication over a discrete arbitrarily varying channel (AVC) when a noisy version of the state is known non-causally at the encoder. The state is chosen by an adversary which knows the coding scheme. A state-myopic encoder observes this state non-causally, though imperfectly, through a noisy discrete memoryless channel (DMC). We first characterize the capacity of this state-dependent channel when the encoder-decoder share randomness unknown to the adversary, i.e., the randomized coding capacity. Next, we show that when only the encoder is allowed to randomize, the capacity remains unchanged when positive. Interesting and well-known special cases of the state-myopic encoder model are also presented.