Minimum Storage Regenerating Codes For All Parameters
Regenerating codes for distributed storage have attracted much research interest in the past decade. Such codes trade the bandwidth needed to repair a failed node with the overall amount of data stored in the network. Minimum storage regenerating (MSR) codes are an important class of optimal regener...
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Zusammenfassung: | Regenerating codes for distributed storage have attracted much research
interest in the past decade. Such codes trade the bandwidth needed to repair a
failed node with the overall amount of data stored in the network. Minimum
storage regenerating (MSR) codes are an important class of optimal regenerating
codes that minimize (first) the amount of data stored per node and (then) the
repair bandwidth. Specifically, an $[n,k,d]$-$(\alpha)$ MSR code $\mathbb{C}$
over $\mathbb{F}_q$ is defined as follows. Using such a code $\mathbb{C}$, a
file $\cal{F}$ consisting of $\alpha k$ symbols over $\mathbb{F}_q$ can be
distributed among $n$ nodes, each storing $\alpha$ symbols, in such a way that:
The file $\cal{F}$ can be recovered by downloading the content of any $k$ of
the $n$ nodes; and the content of any failed node can be reconstructed by
accessing any $d$ of the remaining $n-1$ nodes and downloading $\alpha/(d-k+1)$
symbols from each of these nodes. Unfortunately, explicit constructions of
$[n,k,d]$ MSR codes are known only for certain special cases: either low rate,
namely $k/n0.5$ and
low repair connectivity $k< d |
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DOI: | 10.48550/arxiv.1602.04496 |