Distributed Indirect Source Coding with Decoder Side Information

TL;DR

This paper investigates a distributed source coding problem where multiple correlated sources are encoded independently, and a decoder with side information aims to recover a latent variable within a distortion limit, relevant for semantic communication.

Contribution

It provides bounds on the rate-distortion region and exactly characterizes the rate-distortion function for conditionally independent sources given side information.

Findings

Derived bounds on the rate-distortion region.

Exact characterization for conditionally independent sources.

Applicable to semantic communication and distributed learning.

Abstract

This paper studies a variant of the rate-distortion problem motivated by task-oriented semantic communication and distributed learning problems, where $M$ correlated sources are independently encoded for a central decoder. The decoder has access to a correlated side information in addition to the messages received from the encoders, and aims to recover a latent random variable correlated with the sources observed by the encoders within a given distortion constraint rather than recovering the sources themselves. We provide bounds on the rate-distortion region for this scenario in general, and characterize the rate-distortion function exactly when the sources are conditionally independent given the side information.