Error Exponents in Distributed Hypothesis Testing of Correlations
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isit2019_lower_bou.pdf
Description
Accepted version
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385.64 KB
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Checksum (MD5)
646af9e12905378a0ab3115e5bdb7403
Author(s)
Hadar, Uri
Liu, Jingbo
Polyanskiy, Yury
Shayevitz, Ofer
Date Issued
September 2019
Journal
IEEE International Symposium on Information Theory - Proceedings
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Hadar, Uri, Liu, Jingbo, Polyanskiy, Yury and Shayevitz, Ofer. 2019. "Error Exponents in Distributed Hypothesis Testing of Correlations." IEEE International Symposium on Information Theory - Proceedings, 2019-July.
Version
Author's final manuscript
Abstract
© 2019 IEEE. We study a distributed hypothesis testing problem where two parties observe i.i.d. samples from two ρ-correlated standard normal random variables X and Y. The party that observes the X-samples can communicate R bits per sample to the second party, that observes the Y-samples, in order to test between two correlation values. We investigate the best possible type-II error subject to a fixed type-I error, and derive an upper (impossibility) bound on the associated type-II error exponent. Our techniques include representing the conditional Y-samples as a trajectory of the Ornstein-Uhlenbeck process, and bounding the associated KL divergence using the subadditivity of the Wasserstein distance and the Gaussian Talagrand inequality.
MIT Department
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/ISIT.2019.8849426
