Rate-Distortion with Side-Information at Many Decoders

TL;DR

This paper introduces new bounds for the rate region in multi-stage source coding with side-information, challenges a long-standing conjecture, and provides a counterexample to a classical result in the field.

Contribution

It presents a novel inner bound for the rate region and a new upper bound for the rate-distortion function, along with a counterexample to a well-known theorem.

Findings

New inner bound for the rate region in successive refinement with side-information

New upper bound for the rate-distortion function with multiple decoders

Counterexample to Heegard and Berger's 1985 result

Abstract

We present a new inner bound for the rate region of the $t$-stage successive-refinement problem with side-information. We also present a new upper bound for the rate-distortion function for lossy-source coding with multiple decoders and side-information. Characterising this rate-distortion function is a long-standing open problem, and it is widely believed that the tightest upper bound is provided by Theorem 2 of Heegard and Berger's paper "Rate Distortion when Side Information may be Absent", \emph{IEEE Trans. Inform. Theory}, 1985. We give a counterexample to Heegard and Berger's result.