Rate-Distortion Region for Distributed Indirect Source Coding with Decoder Side Information

TL;DR

This paper characterizes the rate-distortion region for a distributed source coding problem with decoder side information, focusing on latent variable recovery under distortion constraints, relevant for semantic communication and distributed learning.

Contribution

It provides an exact characterization of the rate-distortion function for conditionally independent sources given side information and introduces a numerical algorithm for computation.

Findings

Exact rate-distortion function derived for conditionally independent sources.

Distributed Blahut-Arimoto algorithm developed for numerical computation.

Numerical examples demonstrate the effectiveness of the proposed method.

Abstract

This paper studies a variant of the rate-distortion problem motivated by task-oriented semantic communication and distributed learning systems, where $M$ correlated sources are independently encoded for a central decoder. The decoder has access to correlated side information in addition to the messages received from the encoders and aims to recover a latent random variable under a given distortion constraint, rather than recovering the sources themselves. We characterize the exact rate-distortion function for the case where the sources are conditionally independent given the side information. Furthermore, we develop a distributed Blahut-Arimoto (BA) algorithm to numerically compute the rate-distortion function. Numerical examples are provided to demonstrate the effectiveness of the proposed approach in calculating the rate-distortion region.