# A Fundamental Limit of Distributed Hypothesis Testing Under Memoryless Quantization

arXiv: https://arxiv.org/abs/2206.12232 · HTML: https://mlsanity.com/paper/2206.12232/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 70 references that are in the map.
- First posted on arXiv 24 Jun 2022.

## Builds on (most cited first, 1 of 1)

- [Design of Binary Quantizers for Distributed Detection under Secrecy Constraints](https://mlsanity.com/paper/1410.8100/) (2014)

## Built on by (most cited first, 3 of 3)

- [On the Fusion Strategies for Federated Decision Making](https://mlsanity.com/paper/2303.06109/) (2023)
- [Causal Influence in Federated Edge Inference](https://mlsanity.com/paper/2405.01260/) (2024)
- [Joint Extremum Compression and Detection of a Time-Delayed Signal for Distributed Sensing](https://mlsanity.com/paper/2607.10874/) (2026)

## Abstract (arXiv)

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.