83 research outputs found
A Tight Lower Bound on the Sub-Packetization Level of Optimal-Access MSR and MDS Codes
The first focus of the present paper, is on lower bounds on the
sub-packetization level of an MSR code that is capable of carrying out
repair in help-by-transfer fashion (also called optimal-access property). We
prove here a lower bound on which is shown to be tight for the case
by comparing with recent code constructions in the literature.
We also extend our results to an MDS code over the vector alphabet.
Our objective even here, is on lower bounds on the sub-packetization level
of an MDS code that can carry out repair of any node in a subset of
nodes, where each node is repaired (linear repair) by
help-by-transfer with minimum repair bandwidth. We prove a lower bound on
for the case of . This bound holds for any and
is shown to be tight, again by comparing with recent code constructions in the
literature. Also provided, are bounds for the case .
We study the form of a vector MDS code having the property that we can repair
failed nodes belonging to a fixed set of nodes with minimum repair
bandwidth and in optimal-access fashion, and which achieve our lower bound on
sub-packetization level . It turns out interestingly, that such a code
must necessarily have a coupled-layer structure, similar to that of the Ye-Barg
code.Comment: Revised for ISIT 2018 submissio
An Alternate Construction of an Access-Optimal Regenerating Code with Optimal Sub-Packetization Level
Given the scale of today's distributed storage systems, the failure of an
individual node is a common phenomenon. Various metrics have been proposed to
measure the efficacy of the repair of a failed node, such as the amount of data
download needed to repair (also known as the repair bandwidth), the amount of
data accessed at the helper nodes, and the number of helper nodes contacted.
Clearly, the amount of data accessed can never be smaller than the repair
bandwidth. In the case of a help-by-transfer code, the amount of data accessed
is equal to the repair bandwidth. It follows that a help-by-transfer code
possessing optimal repair bandwidth is access optimal. The focus of the present
paper is on help-by-transfer codes that employ minimum possible bandwidth to
repair the systematic nodes and are thus access optimal for the repair of a
systematic node.
The zigzag construction by Tamo et al. in which both systematic and parity
nodes are repaired is access optimal. But the sub-packetization level required
is where is the number of parities and is the number of
systematic nodes. To date, the best known achievable sub-packetization level
for access-optimal codes is in a MISER-code-based construction by
Cadambe et al. in which only the systematic nodes are repaired and where the
location of symbols transmitted by a helper node depends only on the failed
node and is the same for all helper nodes. Under this set-up, it turns out that
this sub-packetization level cannot be improved upon. In the present paper, we
present an alternate construction under the same setup, of an access-optimal
code repairing systematic nodes, that is inspired by the zigzag code
construction and that also achieves a sub-packetization level of .Comment: To appear in National Conference on Communications 201
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