TY - GEN

T1 - MDS array codes with optimal rebuilding

AU - Tamo, Itzhak

AU - Wang, Zhiying

AU - Bruck, Jehoshua

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80054827910&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2011.6033733

DO - 10.1109/ISIT.2011.6033733

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AN - SCOPUS:80054827910

SN - 9781457705953

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1240

EP - 1244

BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

Y2 - 31 July 2011 through 5 August 2011

ER -