binary array codes are widely used in storage systems to prevent data loss, such as the Redundant array of Independent Disks (RAID). Most designs for such codes, such as Blaum-Roth (BR) codes and Independent-Parity (I...
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binary array codes are widely used in storage systems to prevent data loss, such as the Redundant array of Independent Disks (RAID). Most designs for such codes, such as Blaum-Roth (BR) codes and Independent-Parity (IP) codes, are carried out on the polynomial ring F2[x]/(p-1 2 [ x ] /( p - 1 i =0 xi), i ), where F2 2 is a binary field, and p is a prime number. In this paper, we consider the polynomial ring F2[x]/(p-1 2 [ x ] /(p - 1 i =0 xi tau), i tau ), where p > 1 is an odd number and tau >= 1 is any power of two, and explore variant codes from codes over this polynomial ring. Particularly, the variant codes are derived by mapping parity-check matrices over the polynomial ring to binary parity- check matrices. Specifically, we first propose two classes of variant codes, termed V-ETBR and V-ESIP codes. To make these variant codes binary maximum distance separable (MDS) arraycodes that achieve optimal storage efficiency, this paper then derives the connections between them and their counterparts over polynomial rings. These connections are general, making it easy to construct variant MDS arraycodes from various forms of matrices over polynomial rings. Subsequently, some instances are explicitly constructed based on Cauchy and Vandermonde matrices. In the proposed constructions, both V-ETBR and V-ESIP MDS arraycodes can have any number of parity columns and have the total number of data columns of exponential order with respect to p. In contrast, previous binary MDS arraycodes only have a total number of data columns of linear order with respect to p. This makes the codes proposed in this paper more suitable for application to large-scale storage systems. In terms of computation, two fast syndrome computations are proposed for the Vandermonde-based V-ETBR and V-ESIP MDS arraycodes, both meeting the lowest known asymptotic complexity among MDS codes. Due to the fact that all variant codes are constructed from parity-check matrices over simple binary fields inst
binary Maximum Distance Separable (MDS) arraycodes are widely used in storage systems such as RAID systems that can provide fault tolerance with minimum storage and low computational complexity. As data loss is norma...
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ISBN:
(纸本)9781450366069
binary Maximum Distance Separable (MDS) arraycodes are widely used in storage systems such as RAID systems that can provide fault tolerance with minimum storage and low computational complexity. As data loss is normal in storage system, especially in large-scale distributed storage systems, recent studies have been focused on repair performance. This paper implements a class of binary MDS arraycodes of which the amount of network bandwidth required in repairing a failure is much less than that of the existing repair methods with three parity columns. We conduct experiments and present the performance comparison with other existing works. We show that the implemented binary MDS arraycode can save 40% repair bandwidth compared to Cauchy Reed-Solomon codes. Compared to the existing repair method X-code, the implemented binary MDS arraycode can save 20% repair time and 20% the amount of network bandwidth required in a repair process, respectively.
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