{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T06:34:41Z","timestamp":1774679681581,"version":"3.50.1"},"reference-count":16,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,8]],"date-time":"2019-02-08T00:00:00Z","timestamp":1549584000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002496","name":"Hongik University","doi-asserted-by":"publisher","award":["2017 Hongik University Research Fund"],"award-info":[{"award-number":["2017 Hongik University Research Fund"]}],"id":[{"id":"10.13039\/501100002496","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We establish an universal property of logarithmic loss in the successive refinement problem. If the first decoder operates under logarithmic loss, we show that any discrete memoryless source is successively refinable under an arbitrary distortion criterion for the second decoder. Based on this result, we propose a low-complexity lossy compression algorithm for any discrete memoryless source.<\/jats:p>","DOI":"10.3390\/e21020158","type":"journal-article","created":{"date-parts":[[2019,2,11]],"date-time":"2019-02-11T03:26:01Z","timestamp":1549855561000},"page":"158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Universality of Logarithmic Loss in Successive Refinement"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6346-4182","authenticated-orcid":false,"given":"Albert","family":"No","sequence":"first","affiliation":[{"name":"Department of Electronic and Electrical Engineering, Hongik University, Seoul 04066, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Courtade, T.A., and Wesel, R.D. (August, January 31). Multiterminal source coding with an entropy-based distortion measure. Proceedings of the 2011 IEEE International Symposium on Information Theory Proceedings, St. Petersburg, Russia.","DOI":"10.1109\/ISIT.2011.6033913"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1109\/TIT.2013.2288257","article-title":"Multiterminal Source Coding Under Logarithmic Loss","volume":"60","author":"Courtade","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/TIT.2017.2700860","article-title":"A single-shot approach to lossy source coding under logarithmic loss","volume":"64","author":"Shkel","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","unstructured":"Tishby, N., Pereira, F., and Bialek, W. (1999, January 22\u201324). The information bottleneck method. 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