73 research outputs found

    High-Rate Regenerating Codes Through Layering

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    In this paper, we provide explicit constructions for a class of exact-repair regenerating codes that possess a layered structure. These regenerating codes correspond to interior points on the storage-repair-bandwidth tradeoff, and compare very well in comparison to scheme that employs space-sharing between MSR and MBR codes. For the parameter set (n,k,d=k)(n,k,d=k) with n<2k1n < 2k-1, we construct a class of codes with an auxiliary parameter ww, referred to as canonical codes. With ww in the range nk<w<kn-k < w < k, these codes operate in the region between the MSR point and the MBR point, and perform significantly better than the space-sharing line. They only require a field size greater than w+nkw+n-k. For the case of (n,n1,n1)(n,n-1,n-1), canonical codes can also be shown to achieve an interior point on the line-segment joining the MSR point and the next point of slope-discontinuity on the storage-repair-bandwidth tradeoff. Thus we establish the existence of exact-repair codes on a point other than the MSR and the MBR point on the storage-repair-bandwidth tradeoff. We also construct layered regenerating codes for general parameter set (n,k<d,k)(n,k<d,k), which we refer to as non-canonical codes. These codes also perform significantly better than the space-sharing line, though they require a significantly higher field size. All the codes constructed in this paper are high-rate, can repair multiple node-failures and do not require any computation at the helper nodes. We also construct optimal codes with locality in which the local codes are layered regenerating codes.Comment: 20 pages, 9 figure

    Increasing Availability in Distributed Storage Systems via Clustering

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    We introduce the Fixed Cluster Repair System (FCRS) as a novel architecture for Distributed Storage Systems (DSS), achieving a small repair bandwidth while guaranteeing a high availability. Specifically we partition the set of servers in a DSS into ss clusters and allow a failed server to choose any cluster other than its own as its repair group. Thereby, we guarantee an availability of s1s-1. We characterize the repair bandwidth vs. storage trade-off for the FCRS under functional repair and show that the minimum repair bandwidth can be improved by an asymptotic multiplicative factor of 2/32/3 compared to the state of the art coding techniques that guarantee the same availability. We further introduce Cubic Codes designed to minimize the repair bandwidth of the FCRS under the exact repair model. We prove an asymptotic multiplicative improvement of 0.790.79 in the minimum repair bandwidth compared to the existing exact repair coding techniques that achieve the same availability. We show that Cubic Codes are information-theoretically optimal for the FCRS with 22 and 33 complete clusters. Furthermore, under the repair-by-transfer model, Cubic Codes are optimal irrespective of the number of clusters
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