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Finite Field
Mds Code
Storage System
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MDS Array Codes with Optimal Rebuilding
MDS Array Codes with Optimal Rebuilding,10.1109/ISIT.2011.6033733,Itzhak Tamo,Zhiying Wang,Jehoshua Bruck
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MDS Array Codes with Optimal Rebuilding
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Citations: 3
)
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Itzhak Tamo
,
Zhiying Wang
,
Jehoshua Bruck
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 and 3 , 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 2erasure correcting code, the rebuilding ratio is 1 2 . In general, we construct a new family of rerasure correcting MDS array codes that has optimal rebuilding ratio of 1 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.
Conference:
IEEE International Symposium on Information Theory  ISIT
, vol. abs/1103.3, pp. 12401244, 2011
DOI:
10.1109/ISIT.2011.6033733
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Citation Context
(3)
...The rest of paper is organized as follows: Section II gives definitions and notations, Section III constructs the MDS array codes with optimal rebuilding ratio, and generalizations of the codes are given in Section IV. Due to space limitation, a lot of details are omitted, and the reader is referred to [
19
]...
...A construction in the full version of the paper [
19
] uses a finite field of size at least s + 2, for an MDS sduplication of the code in Theorem 4. For example, in an sduplication code for m = 10, the array is of size 1024 × (11s + 2). For s = 2 and s = 6, the ratio is 0.522 and 0.537 by Theorem 7, the code length is 24 and 68, and the field size needed is 4 and 8, respectively...
...The proof for the lower bound and the rebuilding algorithm are described in [
19
]...
Itzhak Tamo
,
et al.
MDS Array Codes with Optimal Rebuilding
...Codes that minimize reads when repairing systematic nodes were studied in [
8
] for RAIDlike systems (few parity nodes) where storage is minimized instead of bandwidth...
Sameer Pawar
,
et al.
DRESS codes for the storage cloud: Simple randomized constructions
...1 During the submission of this manuscript, two independent works appeared that constructed MDS codes of arbitrary rate that can optimally repair their systematic nodes, see [
14
], [15]...
Dimitris S. Papailiopoulos
,
et al.
Distributed storage codes through Hadamard designs
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Citations
(3)
MDS Array Codes with Optimal Rebuilding
(
Citations: 3
)
Itzhak Tamo
,
Zhiying Wang
,
Jehoshua Bruck
Conference:
IEEE International Symposium on Information Theory  ISIT
, vol. abs/1103.3, pp. 12401244, 2011
DRESS codes for the storage cloud: Simple randomized constructions
Sameer Pawar
,
Nima Noorshams
,
Salim El Rouayheb
,
Kannan Ramchandran
Conference:
IEEE International Symposium on Information Theory  ISIT
, pp. 23382342, 2011
Distributed storage codes through Hadamard designs
Dimitris S. Papailiopoulos
,
Alexandros G. Dimakis
Conference:
IEEE International Symposium on Information Theory  ISIT
, pp. 12301234, 2011