110 research outputs found

    Cooperative Local Repair in Distributed Storage

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    Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems. This paper investigates a generalization of the usual locally repairable codes. In particular, this paper studies a class of codes with the following property: any small set of codeword symbols can be reconstructed (repaired) from a small number of other symbols. This is referred to as cooperative local repair. The main contribution of this paper is bounds on the trade-off of the minimum distance and the dimension of such codes, as well as explicit constructions of families of codes that enable cooperative local repair. Some other results regarding cooperative local repair are also presented, including an analysis for the well-known Hadamard/Simplex codes.Comment: Fixed some minor issues in Theorem 1, EURASIP Journal on Advances in Signal Processing, December 201

    Access vs. Bandwidth in Codes for Storage

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    Maximum distance separable (MDS) codes are widely used in storage systems to protect against disk (node) failures. A node is said to have capacity ll over some field F\mathbb{F}, if it can store that amount of symbols of the field. An (n,k,l)(n,k,l) MDS code uses nn nodes of capacity ll to store kk information nodes. The MDS property guarantees the resiliency to any nkn-k node failures. An \emph{optimal bandwidth} (resp. \emph{optimal access}) MDS code communicates (resp. accesses) the minimum amount of data during the repair process of a single failed node. It was shown that this amount equals a fraction of 1/(nk)1/(n-k) of data stored in each node. In previous optimal bandwidth constructions, ll scaled polynomially with kk in codes with asymptotic rate <1<1. Moreover, in constructions with a constant number of parities, i.e. rate approaches 1, ll is scaled exponentially w.r.t. kk. In this paper, we focus on the later case of constant number of parities nk=rn-k=r, and ask the following question: Given the capacity of a node ll what is the largest number of information disks kk in an optimal bandwidth (resp. access) (k+r,k,l)(k+r,k,l) MDS code. We give an upper bound for the general case, and two tight bounds in the special cases of two important families of codes. Moreover, the bounds show that in some cases optimal-bandwidth code has larger kk than optimal-access code, and therefore these two measures are not equivalent.Comment: This paper was presented in part at the IEEE International Symposium on Information Theory (ISIT 2012). submitted to IEEE transactions on information theor

    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
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