Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Near-optimal Repair of Reed-Solomon Codes with Low Sub-packetization   Minimum storage regenerating (MSR) codes are MDS codes which allow for
recovery of any single erased symbol with optimal repair bandwidth, based on
the smallest possible fraction of the contents downloaded from each of the
other symbols. Recently, certain Reed-Solomon codes were constructed which are
MSR. However, the sub-packetization of these codes is exponentially large,
growing like $n^{\Omega(n)}$ in the constant-rate regime. In this work, we
study the relaxed notion of $\epsilon$-MSR codes, which incur a factor of
$(1+\epsilon)$ higher than the optimal repair bandwidth, in the context of
Reed-Solomon codes. We give constructions of constant-rate $\epsilon$-MSR
Reed-Solomon codes with polynomial sub-packetization of $n^{O(1/\epsilon)}$ and
thereby giving an explicit tradeoff between the repair bandwidth and
sub-packetization.

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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio