Compound Arbitrarily Varying Channels

TL;DR

This paper introduces the compound arbitrarily varying channels (CAVC), a unified model that generalizes and combines aspects of compound and arbitrarily varying channels, analyzing capacity and feasibility for communication under adversarial conditions.

Contribution

It defines the CAVC model, explores its properties, and studies capacity and feasibility for communication and identification problems with deterministic and random coding.

Findings

CAVC unifies compound and AVC models.

Conditions for capacity under different coding schemes.

Feasibility results for communication and identification.

Abstract

We propose a communication model, that we call compound arbitrarily varying channels (CAVC), which unifies and generalizes compound channels and arbitrarily varying channels (AVC). A CAVC can be viewed as a noisy channel with a fixed, but unknown, compound-state and an AVC-state which may vary with every channel use. The AVC-state is controlled by an adversary who is aware of the compound-state. We study three problems in this setting: 'communication', 'communication and compound-state identification', and 'communication or compound-state identification'. For these problems, we study conditions for feasibility and capacity under deterministic coding and random coding.