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A Fundamental Limit of Distributed Hypothesis Testing Under Memoryless Quantization

2022/06/24 by Yunus İnan, Inan, Yunus, Mert Kayaalp +5
Computer Science · Engineering · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Signal Processing (eess.SP) #Wireless Communication Security Techniques #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2206.12232

openalex publication_date 2022/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a distributed hypothesis testing setup where peripheral nodes send quantized data to the fusion center in a memoryless fashion. The 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.

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