A new sufficient condition for sum-rate tightness in quadratic Gaussian multiterminal source coding

TL;DR

This paper introduces a new sufficient condition for the tightness of the Berger-Tung sum-rate bound in quadratic Gaussian multiterminal source coding, expanding the set of known tight cases and guiding future research.

Contribution

It presents a novel sufficient condition for sum-rate tightness, utilizing virtual remote sources and convex optimization, unifying and extending previous results.

Findings

Sets a new sufficient condition for sum-rate tightness.

Unifies all previously known tight cases.

Provides a framework for future partial solutions.

Abstract

This work considers the quadratic Gaussian multiterminal (MT) source coding problem and provides a new sufficient condition for the Berger-Tung sum-rate bound to be tight. The converse proof utilizes a set of virtual remote sources given which the MT sources are block independent with a maximum block size of two. The given MT source coding problem is then related to a set of two-terminal problems with matrix-distortion constraints, for which a new lower bound on the sum-rate is given. Finally, a convex optimization problem is formulated and a sufficient condition derived for the optimal BT scheme to satisfy the subgradient based Karush-Kuhn-Tucker condition. The set of sum-rate tightness problems defined by our new sufficient condition subsumes all previously known tight cases, and opens new direction for a more general partial solution.