Function Computation and Identification over Locally Homomorphic Multiple-Access Channels

TL;DR

This paper introduces locally homomorphic channels and demonstrates their equivalence to function computation codes, leading to improved identification rates over multiple-access channels with independent encoding.

Contribution

It defines locally homomorphic channels, establishes their relation to function computation, and applies these concepts to enhance identification over multiple-access channels.

Findings

Approximate equivalence between locally homomorphic channels and computation codes

Decomposition properties enable independent encoding of messages

Surprising rate improvements in identification with deterministic encoders

Abstract

We develop the notion of a locally homomorphic channel and prove an approximate equivalence between those and codes for computing functions. Further, we derive decomposition properties of locally homomorphic channels which we use to analyze and construct codes where two messages must be encoded independently. This leads to new results for identification and K-identification when all messages are sent over multiple-access channels, which yield surprising rate improvements compared to naive code constructions. In particular, we demonstrate that for the example of identification with deterministic encoders, both encoders can be constructed independently.