Remote Source Coding under Gaussian Noise : Dueling Roles of Power and Entropy Power

TL;DR

This paper derives a new lower bound for the sum-rate-distortion function in a distributed source coding problem with Gaussian noise, revealing a duality between power and entropy power that extends classical results.

Contribution

It introduces a novel lower bound for the CEO problem with Gaussian noise, highlighting the dual roles of power and entropy power in distributed source coding.

Findings

Lower bound matches upper bound for mean-squared error distortion

Bounds reveal a duality between power and entropy power

Results are most significant as the number of agents increases

Abstract

The distributed remote source coding (so-called CEO) problem is studied in the case where the underlying source, not necessarily Gaussian, has finite differential entropy and the observation noise is Gaussian. The main result is a new lower bound for the sum-rate-distortion function under arbitrary distortion measures. When specialized to the case of mean-squared error, it is shown that the bound exactly mirrors a corresponding upper bound, except that the upper bound has the source power (variance) whereas the lower bound has the source entropy power. Bounds exhibiting this pleasing duality of power and entropy power have been well known for direct and centralized source coding since Shannon's work. While the bounds hold generally, their value is most pronounced when interpreted as a function of the number of agents in the CEO problem.