{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T16:28:29Z","timestamp":1776356909603,"version":"3.51.2"},"reference-count":18,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T00:00:00Z","timestamp":1624924800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["715111"],"award-info":[{"award-number":["715111"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>This paper studies binary hypothesis testing with a single sensor that communicates with two decision centers over a memoryless broadcast channel. The main focus lies on the tradeoff between the two type-II error exponents achievable at the two decision centers. In our proposed scheme, we can partially mitigate this tradeoff when the transmitter has a probability larger than 1\/2 to distinguish the alternate hypotheses at the decision centers, i.e., the hypotheses under which the decision centers wish to maximize their error exponents. In the cases where these hypotheses cannot be distinguished at the transmitter (because both decision centers have the same alternative hypothesis or because the transmitter\u2019s observations have the same marginal distribution under both hypotheses), our scheme shows an important tradeoff between the two exponents. The results in this paper thus reinforce the previous conclusions drawn for a setup where communication is over a common noiseless link. Compared to such a noiseless scenario, here, however, we observe that even when the transmitter can distinguish the two hypotheses, a small exponent tradeoff can persist, simply because the noise in the channel prevents the transmitter to perfectly describe its guess of the hypothesis to the two decision centers.<\/jats:p>","DOI":"10.3390\/info12070268","type":"journal-article","created":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T10:52:46Z","timestamp":1624963966000},"page":"268","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Distributed Hypothesis Testing over Noisy Broadcast Channels"],"prefix":"10.3390","volume":"12","author":[{"given":"Sadaf","family":"Salehkalaibar","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran 1433957131, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mich\u00e8le","family":"Wigger","sequence":"additional","affiliation":[{"name":"LTCI, Telecom Paris, IP Paris, 91120 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1109\/TIT.1986.1057194","article-title":"Hypothesis testing with communication constraints","volume":"32","author":"Ahlswede","year":"1986","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1109\/TIT.1987.1057383","article-title":"Hypothesis testing with multiterminal data compression","volume":"33","author":"Han","year":"1987","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","unstructured":"Shimokawa, H., Han, T., and Amari, S.I. (July, January 27). Error bound for hypothesis testing with data compression. Proceedings of the 1994 IEEE International Symposium on Information Theory, Trondheim, Norway."},{"key":"ref_4","unstructured":"Shimokawa, H. (1994). Hypothesis Testing with Multiterminal Data Compression. [Master\u2019s Thesis, University of Tokyo]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4940","DOI":"10.1109\/TIT.2019.2910065","article-title":"On the reliability function of distributed hypothesis testing under optimal detection","volume":"65","author":"Weinberger","year":"2019","journal-title":"IEEE Trans. Inf. 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Proceedings of the 2013 IEEE International Symposium on Information Theory, Istanbul, Turkey.","DOI":"10.1109\/ISIT.2013.6620744"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Katz, G., Piantanida, P., and Debbah, M. (2016, January 10\u201315). Collaborative distributed hypothesis testing with general hypotheses. Proceedings of the 2016 IEEE International Symposium on Information Theory (ISIT), Barcelona, Spain.","DOI":"10.1109\/ISIT.2016.7541590"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2409","DOI":"10.1109\/TCOMM.2018.2798659","article-title":"On hypothesis testing against independence with multiple decision centers","volume":"66","author":"Salehkalaibar","year":"2018","journal-title":"IEEE Trans. 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