MDS Array Codes with Optimal Rebuilding

MDS Array Codes with Optimal Rebuilding,10.1109/ISIT.2011.6033733,Itzhak Tamo,Zhiying Wang,Jehoshua Bruck

MDS Array Codes with Optimal Rebuilding   (Citations: 3)
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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 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 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. 1240-1244, 2011
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    • ...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 s-duplication of the code in Theorem 4. For example, in an s-duplication 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 Tamoet al. MDS Array Codes with Optimal Rebuilding

    • ...Codes that minimize reads when repairing systematic nodes were studied in [8] for RAID-like systems (few parity nodes) where storage is minimized instead of bandwidth...

    Sameer Pawaret 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. Papailiopouloset al. Distributed storage codes through Hadamard designs

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