A Study on Arbitrarily Varying Channels with Causal Side Information at the Encoder

TL;DR

This paper investigates the capacity of arbitrarily varying channels with causal side information at the encoder, deriving bounds and exact capacities under various constraints and conditions for both point-to-point and broadcast channels.

Contribution

It provides new bounds and capacity results for AVCs with causal side information, including conditions for capacity equality and explicit capacity regions for certain channels.

Findings

Derived bounds on random and deterministic code capacities.

Established capacity for AVCs under specific constraints and conditions.

Determined capacity regions for certain broadcast channels.

Abstract

In this work, we study two models of arbitrarily varying channels, when causal side information is available at the encoder in a causal manner. First, we study the arbitrarily varying channel (AVC) with input and state constraints, when the encoder has state information in a causal manner. Lower and upper bounds on the random code capacity are developed. A lower bound on the deterministic code capacity is established in the case of a message-averaged input constraint. In the setting where a state constraint is imposed on the jammer, while the user is under no constraints, the random code bounds coincide, and the random code capacity is determined. Furthermore, for this scenario, a generalized non-symmetrizability condition is stated, under which the deterministic code capacity coincides with the random code capacity. A second model considered in our work is the arbitrarily varying degraded broadcast channel with causal side information at the encoder (without constraints). We establish inner and outer bounds on both the random code capacity region and the deterministic code capacity region. The capacity region is then determined for a class of channels satisfying a condition on the mutual informations between the strategy variables and the channel outputs. As an example, we show that the condition holds for the arbitrarily varying binary symmetric broadcast channel, and we find the corresponding capacity region.