Quantization of Prior Probabilities for Collaborative Distributed Hypothesis Testing

TL;DR

This paper investigates how quantizing prior probabilities affects distributed hypothesis testing, revealing that diverse quantization can outperform identical schemes and establishing equivalences with single-agent setups.

Contribution

It introduces a framework for analyzing quantization of priors in distributed detection, demonstrating the advantages of diverse quantizers and establishing performance equivalences.

Findings

Diverse quantization achieves lower mean Bayes risk error than identical quantization.

Optimal diverse quantization with K cells matches the performance of a single agent with N(K-1)+1 cells.

Results extend to maximum Bayes risk error as the distortion measure.

Abstract

This paper studies the quantization of prior probabilities, drawn from an ensemble, for distributed detection and data fusion. Design and performance equivalences between a team of N agents tied by a fixed fusion rule and a more powerful single agent are obtained. Effects of identical quantization and diverse quantization are compared. Consideration of perceived common risk enables agents using diverse quantizers to collaborate in hypothesis testing, and it is proven that the minimum mean Bayes risk error is achieved by diverse quantization. The comparison shows that optimal diverse quantization with K cells per quantizer performs as well as optimal identical quantization with N(K-1)+1 cells per quantizer. Similar results are obtained for maximum Bayes risk error as the distortion criterion.