Raviv, Netanel (2018) Asymptotically Optimal Regenerating Codes Over Any Field. IEEE Transactions on Information Theory, 64 (11). pp. 7178-7187. ISSN 0018-9448. doi:10.1109/TIT.2018.2815537. https://resolver.caltech.edu/CaltechAUTHORS:20180403-140527057
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Abstract
The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size and, hence, may be hard to implement in practice. By restructuring a code construction by Rashmi et al. , we obtain two explicit families regenerating codes. These codes approach the cut-set bound as the reconstruction degree increases and may be realized over any given finite field if the file size is large enough. Essentially, these codes constitute a constructive proof that the cut-set bound does not imply a field size restriction, unlike some known bounds for ordinary linear codes. The first construction attains the cut-set bound at the MBR point asymptotically for all parameters, whereas the second one attains the cut-set bound at the MSR point asymptotically for low-rate parameters. Even though these codes require a large file size, this restriction is trivially satisfied in most conceivable distributed storage scenarios, that are the prominent motivation for regenerating codes.
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Additional Information: | © 2018 IEEE. Manuscript received September 10, 2017; revised February 28, 2018; accepted March 4, 2018. Date of publication March 13, 2018; date of current version October 18, 2018. N. Raviv was supported in part by the Israeli Science Foundation, Jerusalem, Israel, under Grant 10/12, in part the IBM Ph.D. Fellowship, and in part by the Mitacs organization, through the Globalink Israel-Canada Innovation Initiative. This research was done while the author was a visiting student at the University of Toronto, under the supervision of Prof. F. Kschischang. This paper is a part of his Ph.D. dissertation that was submitted to the Technion under the supervision of Prof. T. Etzion. This paper was presented at the 2017 International Symposium on Information Theory. | ||||||||||||
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Subject Keywords: | Regenerating codes, distributed storage systems, extension fields | ||||||||||||
Issue or Number: | 11 | ||||||||||||
DOI: | 10.1109/TIT.2018.2815537 | ||||||||||||
Record Number: | CaltechAUTHORS:20180403-140527057 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180403-140527057 | ||||||||||||
Official Citation: | N. Raviv, "Asymptotically Optimal Regenerating Codes Over Any Field," in IEEE Transactions on Information Theory, vol. 64, no. 11, pp. 7178-7187, Nov. 2018. doi: 10.1109/TIT.2018.2815537 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 85581 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 03 Apr 2018 21:22 | ||||||||||||
Last Modified: | 15 Nov 2021 20:30 |
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