A Fundamental Limit of Distributed Hypothesis Testing Under Memoryless Quantization

TL;DR

This paper investigates the fundamental limits of distributed hypothesis testing with memoryless quantization, analyzing the tradeoff between communication rate and error decay, and providing bounds and optimal strategies.

Contribution

It characterizes the optimal error decay rates under memoryless quantization constraints and introduces bounds using rate-distortion and water-filling methods.

Findings

Lattice quantization achieves near-optimal performance at high rates.

Derived upper bounds for the tradeoff curve between communication rate and error decay.

Provided analysis for fixed sample recording and sum-rate constrained scenarios.

Abstract

We study a distributed hypothesis testing setup where peripheral nodes send quantized data to the fusion center in a memoryless fashion. The \emph{expected} number of bits sent by each node under the null hypothesis is kept limited. We characterize the optimal decay rate of the mis-detection (type-II error) probability provided that false alarms (type-I error) are rare, and study the tradeoff between the communication rate and maximal type-II error decay rate. We resort to rate-distortion methods to provide upper bounds to the tradeoff curve and show that at high rates lattice quantization achieves near-optimal performance. We also characterize the tradeoff for the case where nodes are allowed to record and quantize a fixed number of samples. Moreover, under sum-rate constraints, we show that an upper bound to the tradeoff curve is obtained with a water-filling solution.