880 research outputs found
Optimal Locally Repairable and Secure Codes for Distributed Storage Systems
This paper aims to go beyond resilience into the study of security and
local-repairability for distributed storage systems (DSS). Security and
local-repairability are both important as features of an efficient storage
system, and this paper aims to understand the trade-offs between resilience,
security, and local-repairability in these systems. In particular, this paper
first investigates security in the presence of colluding eavesdroppers, where
eavesdroppers are assumed to work together in decoding stored information.
Second, the paper focuses on coding schemes that enable optimal local repairs.
It further brings these two concepts together, to develop locally repairable
coding schemes for DSS that are secure against eavesdroppers.
The main results of this paper include: a. An improved bound on the secrecy
capacity for minimum storage regenerating codes, b. secure coding schemes that
achieve the bound for some special cases, c. a new bound on minimum distance
for locally repairable codes, d. code construction for locally repairable codes
that attain the minimum distance bound, and e. repair-bandwidth-efficient
locally repairable codes with and without security constraints.Comment: Submitted to IEEE Transactions on Information Theor
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
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