The Capacity of Causal Adversarial Channels

TL;DR

This paper determines the capacity of a complex adversarial communication channel with constraints, using novel stochastic encoding and a two-phase adversarial strategy, extending previous models to general discrete channels.

Contribution

It provides a comprehensive capacity characterization for a broad class of causal adversarial channels with cost constraints and no shared randomness, introducing new coding and adversarial strategies.

Findings

Capacity characterized for general discrete channels under adversarial conditions.

Achievability via stochastic encoding, list decoding, and disambiguation.

Converse proven using a two-phase 'babble-and-push' adversarial strategy.

Abstract

We characterize the capacity for the discrete-time arbitrarily varying channel with discrete inputs, outputs, and states when (a) the encoder and decoder do not share common randomness, (b) the input and state are subject to cost constraints, (c) the transition matrix of the channel is deterministic given the state, and (d) at each time step the adversary can only observe the current and past channel inputs when choosing the state at that time. The achievable strategy involves stochastic encoding together with list decoding and a disambiguation step. The converse uses a two-phase "babble-and-push" strategy where the adversary chooses the state randomly in the first phase, list decodes the output, and then chooses state inputs to symmetrize the channel in the second phase. These results generalize prior work on specific channels models (additive, erasure) to general discrete alphabets and models.