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Explicit constructions of optimal-access MDS codes with nearly optimal sub-packetization. (arXiv:1605.08630v2 [cs.IT] UPDATED)
来源于:arXiv
An $(n,k,l)$ MDS array code of length $n,$ dimension $k=n-r$ and
sub-packetization $l$ is formed of $l\times n$ matrices over a finite field
$F,$ with every column of the matrix stored on a separate node in a distributed
storage system and viewed as a coordinate of the codeword. Repair of a failed
node can be performed by accessing a set of $d\le n-1$ helper nodes. The code
is said to have the optimal access property if the amount of data accessed at
each of the helper nodes meets a lower bound on this quantity. For
optimal-access MDS codes with $d=n-1,$ the sub-packetization $l$ satisfies the
bound $l\ge r^{(k-1)/r}.$ In our previous work, for any $n$ and $r,$ we
presented an explicit construction of optimal-access MDS codes with
sub-packetization $l=r^{n-1}.$ In this paper we take up the question of
reducing the sub-packetization value $l$ to make it approach the lower bound.
We construct an explicit family of optimal-access codes with $l=r^{\lceil
n/r\rceil},$ which differs from the 查看全文>>