{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:17:26Z","timestamp":1760242646786,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,12,22]],"date-time":"2017-12-22T00:00:00Z","timestamp":1513900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work, we establish a full single-letter characterization of the rate-distortion region of an instance of the Gray\u2013Wyner model with side information at the decoders. Specifically, in this model, an encoder observes a pair of memoryless, arbitrarily correlated, sources \r\n          \r\n            \r\n              \r\n                (\r\n                \r\n                  S\r\n                  1\r\n                  n\r\n                \r\n                ,\r\n                \r\n                  S\r\n                  2\r\n                  n\r\n                \r\n                )\r\n              \r\n            \r\n          \r\n         and communicates with two receivers over an error-free rate-limited link of capacity \r\n          \r\n            \r\n              \r\n                R\r\n                0\r\n              \r\n            \r\n          \r\n        , as well as error-free rate-limited individual links of capacities \r\n          \r\n            \r\n              \r\n                R\r\n                1\r\n              \r\n            \r\n          \r\n         to the first receiver and \r\n          \r\n            \r\n              \r\n                R\r\n                2\r\n              \r\n            \r\n          \r\n         to the second receiver. Both receivers reproduce the source component \r\n          \r\n            \r\n              \r\n                S\r\n                2\r\n                n\r\n              \r\n            \r\n          \r\n         losslessly; and Receiver 1 also reproduces the source component \r\n          \r\n            \r\n              \r\n                S\r\n                1\r\n                n\r\n              \r\n            \r\n          \r\n         lossily, to within some prescribed fidelity level \r\n          \r\n            \r\n              \r\n                D\r\n                1\r\n              \r\n            \r\n          \r\n        . In addition, Receiver 1 and Receiver 2 are equipped, respectively, with memoryless side information sequences \r\n          \r\n            \r\n              \r\n                Y\r\n                1\r\n                n\r\n              \r\n            \r\n          \r\n         and \r\n          \r\n            \r\n              \r\n                Y\r\n                2\r\n                n\r\n              \r\n            \r\n          \r\n        . Important in this setup, the side information sequences are arbitrarily correlated among them, and with the source pair \r\n          \r\n            \r\n              \r\n                (\r\n                \r\n                  S\r\n                  1\r\n                  n\r\n                \r\n                ,\r\n                \r\n                  S\r\n                  2\r\n                  n\r\n                \r\n                )\r\n              \r\n            \r\n          \r\n        ; and are not assumed to exhibit any particular ordering. Furthermore, by specializing the main result to two Heegard\u2013Berger models with successive refinement and scalable coding, we shed light on the roles of the common and private descriptions that the encoder should produce and the role of each of the common and private links. We develop intuitions by analyzing the developed single-letter rate-distortion regions of these models, and discuss some insightful binary examples.<\/jats:p>","DOI":"10.3390\/e20010002","type":"journal-article","created":{"date-parts":[[2017,12,22]],"date-time":"2017-12-22T11:38:04Z","timestamp":1513942684000},"page":"2","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Rate-Distortion Region of a Gray\u2013Wyner Model with Side Information"],"prefix":"10.3390","volume":"20","author":[{"given":"Meryem","family":"Benammar","sequence":"first","affiliation":[{"name":"Department of Electronics Optronics and Signal Processing (DEOS), Institut Superieur de l\u2019A\u00e9ronautique et de l\u2019Espace Supa\u00e9ro (ISAE Supa\u00e9ro), 31400 Toulouse, France"}]},{"given":"Abdellatif","family":"Zaidi","sequence":"additional","affiliation":[{"name":"Mathematics and Algorithmic Sciences Lab, Huawei Technologies France, 92100 Boulogne-Billancourt, France"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1681","DOI":"10.1002\/j.1538-7305.1974.tb02812.x","article-title":"Source coding for a simple network","volume":"53","author":"Gray","year":"1974","journal-title":"Bell Syst. 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Network Information Theory, Cambridge University Press."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/1\/2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:55:10Z","timestamp":1760208910000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/1\/2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,22]]},"references-count":16,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1]]}},"alternative-id":["e20010002"],"URL":"https:\/\/doi.org\/10.3390\/e20010002","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2017,12,22]]}}}