Are Slepian-Wolf Rates Necessary for Distributed Parameter Estimation?

TL;DR

This paper demonstrates that in distributed parameter estimation, it is possible to achieve centralized optimal performance without adhering to Slepian-Wolf rate constraints, challenging previous assumptions.

Contribution

The paper constructs an asymptotically minimum variance unbiased estimator that outperforms traditional rate bounds, showing Slepian-Wolf rates are not necessary for optimal estimation.

Findings

Achieves centralized estimation performance with rates below Slepian-Wolf bounds.

Constructs an estimator matching the centralized optimal variance.

Challenges the necessity of Slepian-Wolf rates in distributed estimation.

Abstract

We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center who will obtain an estimate of a parameter related to observations of all terminals. It is well known that if the transmission rates are in the Slepian-Wolf region, the fusion center can fully recover all observations and hence can construct an estimator having the same performance as that of the centralized case. One natural question is whether Slepian-Wolf rates are necessary to achieve the same estimation performance as that of the centralized case. In this paper, we show that the answer to this question is negative. We establish our result by explicitly constructing an asymptotically minimum variance unbiased estimator (MVUE) that has the same performance as that of the optimal estimator in the centralized case while requiring information rates less than the conditions required in the Slepian-Wolf rate region.