TY - GEN

T1 - Access vs. bandwidth in codes for storage

AU - Tamo, Itzhak

AU - Wang, Zhiying

AU - Bruck, Jehoshua

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84867559996&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2012.6283042

DO - 10.1109/ISIT.2012.6283042

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AN - SCOPUS:84867559996

SN - 9781467325790

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1187

EP - 1191

BT - 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012

T2 - 2012 IEEE International Symposium on Information Theory, ISIT 2012

Y2 - 1 July 2012 through 6 July 2012

ER -