On the Optimal Error Exponent of Type-Based Distributed Hypothesis Testing
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entropy-25-01434.pdf
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1.92 MB
Format
Adobe PDF
Checksum (MD5)
258365ea02c1f04f4b3f5d121729f3ee
Author(s)
Tong, Xinyi
Xu, Xiangxiang
Huang, Shao-Lun
Date Issued
October 10, 2023
Publisher
Multidisciplinary Digital Publishing Institute
Citation
Entropy 25 (10): 1434 (2023)
Version
Final published version
Abstract
Distributed hypothesis testing (DHT) has emerged as a significant research area, but the information-theoretic optimality of coding strategies is often typically hard to address. This paper studies the DHT problems under the type-based setting, which is requested from the popular federated learning methods. Specifically, two communication models are considered: (i) DHT problem over noiseless channels, where each node observes i.i.d. samples and sends a one-dimensional statistic of observed samples to the decision center for decision making; and (ii) DHT problem over AWGN channels, where the distributed nodes are restricted to transmit functions of the empirical distributions of the observed data sequences due to practical computational constraints. For both of these problems, we present the optimal error exponent by providing both the achievability and converse results. In addition, we offer corresponding coding strategies and decision rules. Our results not only offer coding guidance for distributed systems, but also have the potential to be applied to more complex problems, enhancing the understanding and application of DHT in various domains.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.3390/e25101434
