Byzantine Multiple Access Channels -- Part II: Communication With Adversary Identification

TL;DR

This paper studies the problem of identifying a malicious user in a two-user communication system over a multiple access channel, providing capacity characterizations and bounds for secure communication.

Contribution

It introduces the problem of adversary identification in multiple access channels and characterizes the feasible channels and capacity regions without shared randomness.

Findings

Characterization of channels where communication is feasible

Inner and outer bounds on the capacity region

Capacity region equals randomized encoding capacity when non-empty

Abstract

We introduce the problem of determining the identity of a byzantine user (internal adversary) in a communication system. We consider a two-user discrete memoryless multiple access channel where either user may deviate from the prescribed behaviour. Since small deviations may be indistinguishable from the effects of channel noise, it might be overly restrictive to attempt to detect all deviations. When neither user deviates, correct decoding is required. When one user deviates, the decoder must either output a pair of messages of which the message of the non-deviating user is correct or identify the deviating user. The users and the receiver do not share any randomness. The results include a characterization of the set of channels where communication is feasible, and an inner and outer bound on the capacity region. We also show that whenever the rate region has non-empty interior, the capacity region is same as the capacity region under randomized encoding, where each user shares independent randomness with the receiver. We also give an outer bound for this randomized coding capacity region.