{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:24:13Z","timestamp":1750307053855,"version":"3.41.0"},"reference-count":19,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2012,9,1]],"date-time":"2012-09-01T00:00:00Z","timestamp":1346457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100002855","name":"Ministry of Science and Technology of the People's Republic of China","doi-asserted-by":"publisher","award":["2009AA01A403"],"award-info":[{"award-number":["2009AA01A403"]}],"id":[{"id":"10.13039\/501100002855","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["60925006"],"award-info":[{"award-number":["60925006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100002418","name":"Intel Corporation","doi-asserted-by":"publisher","award":["Intel-CRC-2010-06"],"award-info":[{"award-number":["Intel-CRC-2010-06"]}],"id":[{"id":"10.13039\/100002418","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Storage"],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p>Many RAID-6 codes have been proposed in the literature, but each has its limitations. Horizontal code has the ability to adapt to the arbitrary size of a disk array but its high computational complexity is a major shortcoming. In contrast, the computational complexity of vertical code (e.g. X-code) often achieves the theoretical optimality, but vertical code is limited to using a prime number as the size of the disk array In this article, we propose a novel efficient RAID-6 code for arbitrary size of disk array: generalized X-code. We move the redundant elements along their calculation diagonals in X-code onto two specific disks and change two data elements into redundant elements in order to realize our new code. The generalized X-code achieves optimal encoding and updating complexity and low decoding complexity; in addition, it has the ability to adapt to arbitrary size of disk array. Furthermore, we also provide a method for generalizing horizontal code to achieve optimal encoding and updating complexity while keeping the code's original ability to adapt to arbitrary size of disk array.<\/jats:p>","DOI":"10.1145\/2339118.2339121","type":"journal-article","created":{"date-parts":[[2012,9,18]],"date-time":"2012-09-18T14:51:51Z","timestamp":1347979911000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Generalized X-code"],"prefix":"10.1145","volume":"8","author":[{"given":"Xianghong","family":"Luo","sequence":"first","affiliation":[{"name":"Tsinghua University, China"}]},{"given":"Jiwu","family":"Shu","sequence":"additional","affiliation":[{"name":"Tsinghua University, China"}]}],"member":"320","published-online":{"date-parts":[[2012,9,20]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1254882.1254917"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/12.364531"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/18.485722"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/18.746771"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/176979.176981"},{"volume-title":"Proceedings of the 3rd USENIX Conference on File and Storage Technologies (FAST). USENIX","author":"Corbett P.","key":"e_1_2_1_6_1","unstructured":"Corbett , P. , English , B. , Goel , A. , Grcanac , T. , Kleiman , S. , Leong , J. , and Sankar , S . 2004. Row-diagonal redundant for double disk failure correction . In Proceedings of the 3rd USENIX Conference on File and Storage Technologies (FAST). USENIX , Berkeley, CA, 2--15. Corbett, P., English, B., Goel, A., Grcanac, T., Kleiman, S., Leong, J., and Sankar, S. 2004. Row-diagonal redundant for double disk failure correction. In Proceedings of the 3rd USENIX Conference on File and Storage Technologies (FAST). USENIX, Berkeley, CA, 2--15."},{"volume-title":"Proceedings of the 33rd IEEE Sarnoff Symposium. IEEE","author":"Feng J.","key":"e_1_2_1_7_1","unstructured":"Feng , J. , Chen , Y. , and Summerville , D . 2010. EEO: An efficient MDS-like RAID-6 code for parallel implementation . In Proceedings of the 33rd IEEE Sarnoff Symposium. IEEE , Piscataway, NJ, 1--5. Feng, J., Chen, Y., and Summerville, D. 2010. EEO: An efficient MDS-like RAID-6 code for parallel implementation. In Proceedings of the 33rd IEEE Sarnoff Symposium. IEEE, Piscataway, NJ, 1--5."},{"key":"e_1_2_1_8_1","volume-title":"Proceedings of the 4th USENIX Conference on File and Storage Technologies (FAST). USENIX","author":"Hafner J. L.","year":"2005","unstructured":"Hafner , J. L. 2005 . WEAVER codes: Highly fault tolerant erasure codes for storage systems . In Proceedings of the 4th USENIX Conference on File and Storage Technologies (FAST). USENIX , Berkeley, CA, 211--224. Hafner, J. L. 2005. WEAVER codes: Highly fault tolerant erasure codes for storage systems. In Proceedings of the 4th USENIX Conference on File and Storage Technologies (FAST). USENIX, Berkeley, CA, 211--224."},{"key":"e_1_2_1_9_1","unstructured":"Hafner J. M. Deenadhayalan V. Kanungo T. and Rao K. 2004. Performance metrics for erasure codes in storage systems. Tech. rep. RJ 10321 IBM Research San Jose CA.  Hafner J. M. Deenadhayalan V. Kanungo T. and Rao K. 2004. Performance metrics for erasure codes in storage systems. Tech. rep. RJ 10321 IBM Research San Jose CA."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1542275.1542326"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1480439.1480444"},{"volume-title":"Proceedings of the IEEE COMPCON Conference. IEEE","author":"Patterson D. A.","key":"e_1_2_1_12_1","unstructured":"Patterson , D. A. , Chen , P. , Gibson , G. , and Katz , R. H . 1989. Introduction to redundant arrays of inexpensive disks . In Proceedings of the IEEE COMPCON Conference. IEEE , Los Alamitos, CA, 112--117. Patterson, D. A., Chen, P., Gibson, G., and Katz, R. H. 1989. Introduction to redundant arrays of inexpensive disks. In Proceedings of the IEEE COMPCON Conference. IEEE, Los Alamitos, CA, 112--117."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/50202.50214"},{"volume-title":"Proceedings of 5th USENIX Conference on File and Storage Technologies (FAST). USENIX","author":"Pinheiro E.","key":"e_1_2_1_14_1","unstructured":"Pinheiro , E. , Weber , W. D. , and Barroso , L. A . 2007. Failure trends in a large disk drive population . In Proceedings of 5th USENIX Conference on File and Storage Technologies (FAST). USENIX , Berkeley, CA, 17--28. Pinheiro, E., Weber, W. D., and Barroso, L. A. 2007. Failure trends in a large disk drive population. In Proceedings of 5th USENIX Conference on File and Storage Technologies (FAST). USENIX, Berkeley, CA, 17--28."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.5555\/1364813.1364820"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1177\/1094342009106191"},{"key":"e_1_2_1_17_1","unstructured":"Schroeder B. and Gibson G. A. 2007. Disk failures in the real world: What does an MTTF of 1 000 000 hours mean to you&quest; In Proceedings of the 5th USENIX Conference on File and Storage Technologies (FAST). USENIX Berkeley CA 1--16.   Schroeder B. and Gibson G. A. 2007. Disk failures in the real world: What does an MTTF of 1 000 000 hours mean to you&quest; In Proceedings of the 5th USENIX Conference on File and Storage Technologies (FAST). USENIX Berkeley CA 1--16."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/18.782102"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1109\/18.746809"}],"container-title":["ACM Transactions on Storage"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2339118.2339121","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2339118.2339121","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T09:21:08Z","timestamp":1750238468000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2339118.2339121"}},"subtitle":["An efficient RAID-6 code for arbitrary size of disk array"],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["10.1145\/2339118.2339121"],"URL":"https:\/\/doi.org\/10.1145\/2339118.2339121","relation":{},"ISSN":["1553-3077","1553-3093"],"issn-type":[{"type":"print","value":"1553-3077"},{"type":"electronic","value":"1553-3093"}],"subject":[],"published":{"date-parts":[[2012,9]]},"assertion":[{"value":"2011-04-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-05-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-09-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}