{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:12:37Z","timestamp":1760242357393,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2017,5,24]],"date-time":"2017-05-24T00:00:00Z","timestamp":1495584000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["396\/11"],"award-info":[{"award-number":["396\/11"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Research Council (ERC) through Starting Grant BEACON","award":["677854"],"award-info":[{"award-number":["677854"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This work studies the relationship between the energy allocated for transmitting a pair of correlated Gaussian sources over a two-user Gaussian broadcast channel with noiseless channel output feedback (GBCF) and the resulting distortion at the receivers. Our goal is to characterize the minimum transmission energy required for broadcasting a pair of source samples, such that each source can be reconstructed at its respective receiver to within a target distortion, when the source-channel bandwidth ratio is not restricted. This minimum transmission energy is defined as the energy-distortion tradeoff (EDT). We derive a lower bound and three upper bounds on the optimal EDT. For the upper bounds, we analyze the EDT of three transmission schemes: two schemes are based on separate source-channel coding and apply encoding over multiple samples of source pairs, and the third scheme is a joint source-channel coding scheme that applies uncoded linear transmission on a single source-sample pair and is obtained by extending the Ozarow\u2013Leung (OL) scheme. Numerical simulations show that the EDT of the OL-based scheme is close to that of the better of the two separation-based schemes, which makes the OL scheme attractive for energy-efficient, low-latency and low-complexity source transmission over GBCFs.<\/jats:p>","DOI":"10.3390\/e19060243","type":"journal-article","created":{"date-parts":[[2017,5,24]],"date-time":"2017-05-24T07:29:42Z","timestamp":1495610982000},"page":"243","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Energy-Distortion Tradeoff of Gaussian Broadcast Channels with Feedback"],"prefix":"10.3390","volume":"19","author":[{"given":"Yonathan","family":"Murin","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yonatan","family":"Kaspi","sequence":"additional","affiliation":[{"name":"Goldman Sachs, New York, NY 10282, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ron","family":"Dabora","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Be\u2019er-Sheva 8410501, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deniz","family":"G\u00fcnd\u00fcz","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3153","DOI":"10.1109\/TIT.2012.2184912","article-title":"Energy-distortion tradeoffs in Gaussian joint source-channel coding problems","volume":"58","author":"Jain","year":"2012","journal-title":"IEEE Trans. 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