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Asymptotically Optimal Regenerating Codes Over Any Field

Raviv, Netanel (2018) Asymptotically Optimal Regenerating Codes Over Any Field. IEEE Transactions on Information Theory, 64 (11). pp. 7178-7187. ISSN 0018-9448. http://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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TIT.2018.2815537DOIArticle
http://ieeexplore.ieee.org/document/8315050PublisherArticle
https://arxiv.org/abs/1609.06420arXivDiscussion Paper
ORCID:
AuthorORCID
Raviv, Netanel0000-0002-1686-1994
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.
Funders:
Funding AgencyGrant Number
Israel Science Foundation10/12
IBMUNSPECIFIED
MITACSUNSPECIFIED
Globalink Israel-Canada InnovationUNSPECIFIED
Subject Keywords:Regenerating codes, distributed storage systems, extension fields
Record Number:CaltechAUTHORS:20180403-140527057
Persistent URL:http://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:25 Oct 2018 16:37

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