Identification via the Broadcast Channel

TL;DR

This paper characterizes the identification capacity region of the two-receiver broadcast channel, showing it matches certain mutual information bounds and introducing new code constructions, with extensions to feedback and three-receiver cases.

Contribution

It provides the first characterization of the ID capacity region for the two-receiver broadcast channel and introduces a novel ID code construction for single-user channels.

Findings

ID capacity region equals the set of rate-pairs bounded by mutual information.

Deterministic encoders achieve the capacity region's interior.

Extensions to feedback and three-receiver channels yield tight inner bounds.

Abstract

The identification (ID) capacity region of the two-receiver broadcast channel (BC) is shown to be the set of rate-pairs for which, for some distribution on the channel input, each receiver's ID rate does not exceed the mutual information between the channel input and the channel output that it observes. Moreover, the capacity region's interior is achieved by codes with deterministic encoders. The results are obtained under the average-error criterion, which requires that each receiver reliably identify its message whenever the message intended for the other receiver is drawn at random. They hold also for channels whose transmission capacity region is to-date unknown. Key to the proof is a new ID code construction for the single-user channel. Extensions to the BC with one-sided feedback and the three-receiver BC are also discussed: inner bounds on their ID capacity regions are obtained, and those are shown to be in some cases tight.