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MDS Array Codes with Optimal Rebuilding

Tamo, Itzhak and Wang, Zhiying and Bruck, Jehoshua (2011) MDS Array Codes with Optimal Rebuilding. In: 2011 IEEE International Symposium on Information Theory Proceedings. IEEE , Piscataway, NJ, pp. 1240-1244. ISBN 978-1-4577-0596-0. https://resolver.caltech.edu/CaltechAUTHORS:20120406-093959188

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Abstract

MDS array codes are widely used in storage systems to protect data against erasures. We address the rebuilding ratio problem, namely, in the case of erasures, what is the the fraction of the remaining information that needs to be accessed in order to rebuild exactly the lost information? It is clear that when the number of erasures equals the maximum number of erasures that an MDS code can correct then the rebuilding ratio is 1 (access all the remaining information). However, the interesting (and more practical) case is when the number of erasures is smaller than the erasure correcting capability of the code. For example, consider an MDS code that can correct two erasures: What is the smallest amount of information that one needs to access in order to correct a single erasure? Previous work showed that the rebuilding ratio is bounded between 1/2 and 3/4, however, the exact value was left as an open problem. In this paper, we solve this open problem and prove that for the case of a single erasure with a 2-erasure correcting code, the rebuilding ratio is 1/2. In general, we construct a new family of r-erasure correcting MDS array codes that has optimal rebuilding ratio of 1/r in the case of a single erasure. Our array codes have efficient encoding and decoding algorithms (for the case r = 2 they use a finite field of size 3) and an optimal update property.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ISIT.2011.6033733DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6033733PublisherArticle
http://arxiv.org/abs/1103.3737arXivDiscussion Paper
ORCID:
AuthorORCID
Bruck, Jehoshua0000-0001-8474-0812
Additional Information:© 2011 IEEE. Date of Current Version: 03 October 2011. This work was supported in part by the NSF grant ECCS-0802107 and by an NSF-NRI award.
Funders:
Funding AgencyGrant Number
NSFECCS-0802107
NSF-NRI AwardUNSPECIFIED
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INSPEC Accession Number 12300048
Record Number:CaltechAUTHORS:20120406-093959188
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120406-093959188
Official Citation:Tamo, I.; Zhiying Wang; Bruck, J.; , "MDS array codes with optimal rebuilding," Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on , vol., no., pp.1240-1244, July 31 2011-Aug. 5 2011 doi: 10.1109/ISIT.2011.6033733 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6033733&isnumber=6033677
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:30006
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:06 Apr 2012 16:50
Last Modified:22 Nov 2019 09:58

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