Byzantine Multiple Access Channels -- Part I: Reliable Communication

TL;DR

This paper investigates reliable communication over multi-user channels with potential adversarial users, characterizing capacity regions under various adversarial scenarios and code types, extending classical results to adversarial settings.

Contribution

It provides the first capacity characterizations for multi-user MACs with adversarial users, including deterministic and randomized coding strategies, generalizing to multiple users and adversarial subsets.

Findings

Capacity region for 2-user MAC derived from point-to-point AVC.

Capacity region for 3-user MAC with at most one malicious user characterized.

Generalized capacity results for k-user MAC with adversaries controlling subsets.

Abstract

We study communication over a Multiple Access Channel (MAC) where users can possibly be adversarial. The receiver is unaware of the identity of the adversarial users (if any). When all users are non-adversarial, we want their messages to be decoded reliably. When a user behaves adversarially, we require that the honest users' messages be decoded reliably. An adversarial user can mount an attack by sending any input into the channel rather than following the protocol. It turns out that the $2$-user MAC capacity region follows from the point-to-point Arbitrarily Varying Channel (AVC) capacity. For the $3$-user MAC in which at most one user may be malicious, we characterize the capacity region for deterministic codes and randomized codes (where each user shares an independent random secret key with the receiver). These results are then generalized for the $k$-user MAC where the adversary may control all users in one out of a collection of given subsets.