{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:17:33Z","timestamp":1760231853501,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T00:00:00Z","timestamp":1651017600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["CCF-1908957"],"award-info":[{"award-number":["CCF-1908957"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In a traditional distributed storage system, a source can be restored perfectly when a certain subset of servers is contacted. The coding is independent of the contents of the source. This paper considers instead a lossy source coding version of this problem where the more servers that are contacted, the higher the quality of the restored source. An example could be video stored on distributed storage. In information theory, this is called the multiple description problem, where the distortion depends on the number of descriptions received. The problem considered in this paper is how to restore the system operation when one of the servers fail and a new server replaces it, that is, repair. The requirement is that the distortions in the restored system should be no more than in the original system. The question is how many extra bits are needed for repair. We find an achievable rate and show that this is optimal in certain cases. One conclusion is that it is necessary to design the multiple description codes with repair in mind; just using an existing multiple description code results in unnecessary high repair rates.<\/jats:p>","DOI":"10.3390\/e24050612","type":"journal-article","created":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T13:40:57Z","timestamp":1651066857000},"page":"612","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Repair Rates for Multiple Descriptions on Distributed Storage"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1472-4953","authenticated-orcid":false,"given":"Anders","family":"H\u00f8st-Madsen","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, University of Hawaii Manoa, Honolulu, HI 96822, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heecheol","family":"Yang","sequence":"additional","affiliation":[{"name":"Division of Computer Convergence, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minchul","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jungwoo","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4539","DOI":"10.1109\/TIT.2010.2054295","article-title":"Network Coding for Distributed Storage Systems","volume":"56","author":"Dimakis","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1109\/TIT.1982.1056588","article-title":"Achievable rates for multiple descriptions","volume":"28","author":"Gamal","year":"1982","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","unstructured":"Gamal, A.E., and Kim, Y.H. (2011). Network Information Theory, Cambridge University Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1109\/TIT.2005.844063","article-title":"n-channel symmetric multiple descriptions-part II:An achievable rate-distortion region","volume":"51","author":"Puri","year":"2005","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chan, T.H., and Ho, S.W. (2013, January 7\u201312). Robust multiple description coding\u2014Joint Coding for source and storage. Proceedings of the 2013 IEEE International Symposium on Information Theory, Istanbul, Turkey.","DOI":"10.1109\/ISIT.2013.6620539"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kapetanovic, D., Chatzinotas, S., and Ottersten, B. (2014, January 10\u201314). Index assignment for multiple description repair in distributed storage systems. Proceedings of the 2014 IEEE International Conference on Communications (ICC), Sydney, Australia.","DOI":"10.1109\/ICC.2014.6883929"},{"key":"ref_7","unstructured":"H\u00f8st-Madsen, A., Yang, H., Kim, M., and Lee, J. (2020, January 24\u201327). Repair of Multiple Descriptions on Distributed Storage. Proceedings of the ISITA\u20192020, Honolulu, HI, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1109\/TIT.2007.896880","article-title":"Vector Gaussian Multiple Description With Individual and Central Receivers","volume":"53","author":"Wang","year":"2007","journal-title":"IEEE Trans. Inf. 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Theory"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1109\/TIT.2015.2506586","article-title":"Combinatorial Message Sharing and a New Achievable Region for Multiple Descriptions","volume":"62","author":"Viswanatha","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1109\/TIT.2003.821998","article-title":"n-channel symmetric multiple descriptions\u2014Part I: (n, k) source-channel erasure codes","volume":"50","author":"Pradhan","year":"2004","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","unstructured":"Cover, T., and Thomas, J. (2006). Information Theory, John Wiley. [2nd ed.]."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/5\/612\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:02:02Z","timestamp":1760137322000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/5\/612"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,27]]},"references-count":14,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["e24050612"],"URL":"https:\/\/doi.org\/10.3390\/e24050612","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,4,27]]}}}