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Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction

Rashmi, KV and Shah, Nihar B and Kumar, Vijay P (2011) Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction. In: IEEE Transactions on Information Theory, 57 (8). pp. 5227-5239.

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Abstract

Regenerating codes are a class of distributed storage codes that allow for efficient repair of failed nodes, as compared to traditional erasure codes. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that a failed node be repaired by connecting to any d nodes. The amount of data downloaded for repair is typically much smaller than the size of the source data. Previous constructions of exact-regenerating codes have been confined to the case n = d + 1. In this paper, we present optimal, explicit constructions of (a) Minimum Bandwidth Regenerating (MBR) codes for all values of [n, k, d] and (b) Minimum Storage Regenerating (MSR) codes for all [n, k, d >= 2k - 2], using a new product-matrix framework. The product-matrix framework is also shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the network, to be chosen independent of the other parameters. The paper also contains a simpler description, in the product-matrix framework, of a previously constructed MSR code with [n = d + 1, k, d >= 2k - 1].

Item Type: Journal Article
Additional Information: Copyright 2011 IEEE. Personal use of this material is permitted.However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: Distributed storage;interference alignment;network coding; node repair;partial data recovery;product-matrix framework; regenerating codes
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 09 Nov 2011 05:55
Last Modified: 09 Nov 2011 05:55
URI: http://eprints.iisc.ernet.in/id/eprint/41941

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