The Three-Terminal Interactive Lossy Source Coding Problem

TL;DR

This paper extends the two-terminal interactive lossy source coding framework to three nodes, deriving an inner bound for the rate-distortion region that unifies and generalizes previous results, revealing new insights and open challenges.

Contribution

It introduces a comprehensive inner bound for the three-terminal interactive lossy source coding problem, generalizing Kaspi's two-terminal work and unifying multiple prior results.

Findings

Derived an inner bound for the three-node rate-distortion region.

Unified several previous source coding results under a common framework.

Identified new rate-distortion regions for specific lossy source coding scenarios.

Abstract

The three-node multiterminal lossy source coding problem is investigated. We derive an inner bound to the general rate-distortion region of this problem which is a natural extension of the seminal work by Kaspi'85 on the interactive two-terminal source coding problem. It is shown that this (rather involved) inner bound contains several rate-distortion regions of some relevant source coding settings. In this way, besides the non-trivial extension of the interactive two terminal problem, our results can be seen as a generalization and hence unification of several previous works in the field. Specializing to particular cases we obtain novel rate-distortion regions for several lossy source coding problems. We finish by describing some of the open problems and challenges. However, the general three-node multiterminal lossy source coding problem seems to offer a formidable mathematical complexity.