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Access vs. Bandwidth in Codes for Storage

Tamo, Itzhak and Wang, Zhiying and Bruck, Jehoshua (2012) Access vs. Bandwidth in Codes for Storage. In: 2012 IEEE International Symposium on Information Theory Proceedings (ISIT). IEEE , Piscataway, NJ, pp. 1187-1191. ISBN 978-1-4673-2580-6. https://resolver.caltech.edu/CaltechAUTHORS:20120829-092120549

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Abstract

Maximum distance separable (MDS) codes are widely used in storage systems to protect against disks (nodes) failures. An (n, k, l) MDS code uses n nodes of capacity l to store k information nodes. The MDS property guarantees the resiliency to any n − k node failures. An optimal bandwidth (resp. optimal access) MDS code communicates (resp. accesses) the minimum amount of data during the recovery process of a single failed node. It was shown that this amount equals a fraction of 1/(n − k) of data stored in each node. In previous optimal bandwidth constructions, l scaled polynomially with k in codes with asymptotic rate < 1. Moreover, in constructions with constant number of parities, i.e. rate approaches 1, l scaled exponentially w.r.t. k. In this paper we focus on the practical case of n − k = 2, and ask the following question: Given the capacity of a node l what is the largest (w.r.t. k) optimal bandwidth (resp. access) (k + 2, k, l) MDS code. We give an upper bound for the general case, and two tight bounds in the special cases of two important families of codes.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6283042PublisherArticle
http://dx.doi.org/10.1109/ISIT.2012.6283042DOIArticle
http://arxiv.org/abs/1303.3668arXivDiscussion Paper
ORCID:
AuthorORCID
Bruck, Jehoshua0000-0001-8474-0812
Additional Information:© 2012 IEEE. Date of Current Version: 27 August 2012; Issue Date: 1-6 July 2012. This work was partially supported by an NSF grant ECCS- 0801795 and a BSF grant 2010075.
Funders:
Funding AgencyGrant Number
NSFECCS-0801795
Binational Science Foundation (USA-Israel)2010075
DOI:10.1109/ISIT.2012.6283042
Record Number:CaltechAUTHORS:20120829-092120549
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120829-092120549
Official Citation:Tamo, Itzhak; Wang, Zhiying; Bruck, Jehoshua; , "Access vs. bandwidth in codes for storage," Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on , vol., no., pp.1187-1191, 1-6 July 2012 doi: 10.1109/ISIT.2012.6283042
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33642
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:29 Aug 2012 16:59
Last Modified:09 Nov 2021 21:36

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