Rateless codes for AVC models

TL;DR

This paper introduces rateless coding strategies for arbitrarily varying channels, allowing adaptive rates based on adversarial actions, and achieves capacity results with limited shared randomness.

Contribution

It develops rateless codes for AVCs, including models where the adversary's state depends on the codeword, and establishes achievable capacities with minimal common randomness.

Findings

Achieves capacity for AVC with state depending on codeword.

Constructs rateless codes requiring limited shared randomness.

Uses list decoding in the randomized coding strategy.

Abstract

The arbitrarily varying channel (AVC) is a channel model whose state is selected maliciously by an adversary. Fixed-blocklength coding assumes a worst-case bound on the adversary's capabilities, which leads to pessimistic results. This paper defines a variable-length perspective on this problem, for which achievable rates are shown that depend on the realized actions of the adversary. Specifically, rateless codes are constructed which require a limited amount of common randomness. These codes are constructed for two kinds of AVC models. In the first the channel state cannot depend on the channel input, and in the second it can. As a byproduct, the randomized coding capacity of the AVC with state depending on the transmitted codeword is found and shown to be achievable with a small amount of common randomness. The results for this model are proved using a randomized strategy based on list decoding.