{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:56:30Z","timestamp":1760241390942,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,8]],"date-time":"2018-02-08T00:00:00Z","timestamp":1518048000000},"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 relax the usual separability assumption made in rate-distortion literature and propose    f   -separable distortion measures, which are well suited to model non-linear penalties. The main insight behind    f   -separable distortion measures is to define an n-letter distortion measure to be an    f   -mean of single-letter distortions. We prove a rate-distortion coding theorem for stationary ergodic sources with    f   -separable distortion measures, and provide some illustrative examples of the resulting rate-distortion functions. Finally, we discuss connections between    f   -separable distortion measures, and the subadditive distortion measure previously proposed in literature.<\/jats:p>","DOI":"10.3390\/e20020111","type":"journal-article","created":{"date-parts":[[2018,2,9]],"date-time":"2018-02-09T12:46:27Z","timestamp":1518180387000},"page":"111","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Coding Theorem for f-Separable Distortion Measures"],"prefix":"10.3390","volume":"20","author":[{"given":"Yanina","family":"Shkel","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergio","family":"Verd\u00fa","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,8]]},"reference":[{"key":"ref_1","unstructured":"Shannon, C.E. (1993). Coding Theorems for a Discrete Source with a Fidelity Criterion Institute of Radio Engineers, International Convention Record, vol. 7, 1959. Claude E. Shannon: Collected Papers, Wiley-IEEE Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1007\/978-94-011-3030-1_17","article-title":"On the Notion of Mean","volume":"Volume 25","author":"Tikhomirov","year":"1991","journal-title":"Selected Works of A. N. Kolmogorov"},{"key":"ref_3","first-page":"547","article-title":"On Measures of Entropy and Information; Contributions to the Theory of Statistics","volume":"Volume 1","year":"1961","journal-title":"Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/S0019-9958(65)90332-3","article-title":"A coding theorem and R\u00e9nyi\u2019s entropy","volume":"8","author":"Campbell","year":"1965","journal-title":"Inf. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF00537132","article-title":"Definition of entropy by means of a coding problem","volume":"6","author":"Campbell","year":"1966","journal-title":"Z. Wahrscheinlichkeitstheorie Verwandte Gebiete"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/S0019-9958(79)90521-7","article-title":"Variable-length source coding with a cost depending only on the code word length","volume":"41","author":"Kieffer","year":"1979","journal-title":"Inf. Control"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1109\/18.481781","article-title":"An inequality on guessing and its application to sequential decoding","volume":"42","author":"Arikan","year":"1996","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5065","DOI":"10.1109\/TIT.2014.2329490","article-title":"Encoding Tasks and R\u00e9nyi Entropy","volume":"60","author":"Bunte","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1109\/18.669158","article-title":"Guessing subject to distortion","volume":"44","author":"Arikan","year":"1998","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Gray, R.M. (2011). Entropy and Information Theory, Springer. [2nd ed.].","DOI":"10.1007\/978-1-4419-7970-4"},{"key":"ref_11","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley-Interscience. [2nd ed.]."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/18.75240","article-title":"Strong converses in source coding relative to a fidelity criterion","volume":"37","author":"Kieffer","year":"1991","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Han, T.S. (2003). Information-Spectrum Methods in Information Theory, Springer.","DOI":"10.1007\/978-3-662-12066-8"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1109\/18.481779","article-title":"Simulation of random processes and rate-distortion theory","volume":"42","author":"Steinberg","year":"1996","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Dytso, A., Bustin, R., Poor, H.V., and Shitz, S.S. (2017, January 25\u201330). On additive channels with generalized Gaussian noise. Proceedings of the 2017 IEEE International Symposium on Information Theory (ISIT), Aachen, Germany.","DOI":"10.1109\/ISIT.2017.8006563"},{"key":"ref_16","unstructured":"Verd\u00fa, S. (2015). ELE528: Information Theory Lecture Notes, Princeton University."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/2\/111\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:54:15Z","timestamp":1760194455000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/2\/111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,8]]},"references-count":16,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,2]]}},"alternative-id":["e20020111"],"URL":"https:\/\/doi.org\/10.3390\/e20020111","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,2,8]]}}}