Distributed Indirect Source Coding with Decoder Side Information

TL;DR

This work studies a distributed indirect rate-distortion problem with decoder side information, modeling the semantic source as a Bayesian network of $(X_1,X_2,X_3,Z,F)$ and seeking to reconstruct a latent variable within distortion constraints. It develops an achievable region using auxiliary variables $(W_1,W_2,W_3)$ in a Wyner–Ziv–style framework, alongside a general outer bound, and proves these bounds coincide for BN-structured sources to yield an exact rate-distortion function. The results extend classical Slepian–Wolf and Wyner–Ziv concepts to multi-source with decoder side information and provide principled guidance for task-oriented semantic communication and distributed learning applications.

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.

Figures (2)

• Figure 1: The conditional dependence relations among $X_1, X_2, X_3, Z, F$.
• Figure 2: Separate compression of three sources with side information at receiver.