TY - GEN
T1 - Error Exponents in Distributed Hypothesis Testing of Correlations
AU - Hadar, Uri
AU - Liu, Jingbo
AU - Polyanskiy, Yury
AU - Shayevitz, Ofer
N1 - Funding Information:
Order of authors is alphabetical. U.H. and O.S. {emails: uri-hadar@mail.tau.ac.il, ofersha@eng.tau.ac.il} are with the Department of Electrical Engineering–Systems, Tel Aviv University, Tel Aviv, Israel. J.L. and Y.P. {emails: jingbo@mit.edu, yp@mit.edu} are with the Institute for Data, Systems, and Society and the Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. This material is based upon work supported by the National Science Foundation CAREER award under grant agreement CCF-12-53205, the Center for Science of Information (CSoI), an NSF Science and Technology Center, under grant agreement CCF-09-39370, the European Research Council, under grant agreement 639573, the Israeli Science Foundation, under grant agreement 1367/14, and the Yitzhak and Chaya Weinstein Research Institute for Signal Processing.
PY - 2019/7
Y1 - 2019/7
N2 - 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.
AB - 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.
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U2 - 10.1109/ISIT.2019.8849426
DO - 10.1109/ISIT.2019.8849426
M3 - Conference contribution
AN - SCOPUS:85073148377
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2674
EP - 2678
BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019
Y2 - 7 July 2019 through 12 July 2019
ER -