Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and
  MBR Points via a Product-Matrix Construction   Regenerating codes are a class of distributed storage codes that optimally
trade the bandwidth needed for repair of a failed node with the amount of data
stored per node of the network. Minimum Storage Regenerating (MSR) codes
minimize first, the amount of data stored per node, and then the repair
bandwidth, while Minimum Bandwidth Regenerating (MBR) codes carry out the
minimization in the reverse order. 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 repair of a failed node be made possible by connecting
(using links of lesser capacity) to any d nodes. Previous, explicit and general
constructions of exact-regenerating codes have been confined to the case n=d+1.
In this paper, we present optimal, explicit constructions of MBR codes for all
feasible values of [n, k, d] and MSR codes for all [n, k, d >= 2k-2], using a
product-matrix framework. The particular product-matrix nature of the
constructions is 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 distributed storage 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 in which the parameter d satisfies [n=d+1, k, d >= 2k-1].

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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics