Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 57, Issue 8, Pages 5227-5239Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2011.2159049
Keywords
Distributed storage; interference alignment; network coding; node repair; partial data recovery; product-matrix framework; regenerating codes
Funding
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [0964507] Funding Source: National Science Foundation
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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].
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