5,533 research outputs found
Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage
Erasure coding techniques are used to increase the reliability of distributed
storage systems while minimizing storage overhead. Also of interest is
minimization of the bandwidth required to repair the system following a node
failure. In a recent paper, Wu et al. characterize the tradeoff between the
repair bandwidth and the amount of data stored per node. They also prove the
existence of regenerating codes that achieve this tradeoff.
In this paper, we introduce Exact Regenerating Codes, which are regenerating
codes possessing the additional property of being able to duplicate the data
stored at a failed node. Such codes require low processing and communication
overheads, making the system practical and easy to maintain. Explicit
construction of exact regenerating codes is provided for the minimum bandwidth
point on the storage-repair bandwidth tradeoff, relevant to
distributed-mail-server applications. A subspace based approach is provided and
shown to yield necessary and sufficient conditions on a linear code to possess
the exact regeneration property as well as prove the uniqueness of our
construction.
Also included in the paper, is an explicit construction of regenerating codes
for the minimum storage point for parameters relevant to storage in
peer-to-peer systems. This construction supports a variable number of nodes and
can handle multiple, simultaneous node failures. All constructions given in the
paper are of low complexity, requiring low field size in particular.Comment: 7 pages, 2 figures, in the Proceedings of Allerton Conference on
Communication, Control and Computing, September 200
On Epsilon-MSCR Codes for Two Erasures
Cooperative regenerating codes are regenerating codes designed to tradeoff
storage for repair bandwidth in case of multiple node failures. Minimum storage
cooperative regenerating (MSCR) codes are a class of cooperative regenerating
codes which achieve the minimum storage point of the tradeoff. Recently, these
codes have been constructed for all possible parameters , where
erasures are repaired by contacting any surviving nodes. However, these
constructions have very large sub-packetization. -MSR codes are a
class of codes introduced to tradeoff subpacketization level for a slight
increase in the repair bandwidth for the case of single node failures. We
introduce the framework of -MSCR codes which allow for a similar
tradeoff for the case of multiple node failures. We present a construction of
-MSCR codes, which can recover from two node failures, by
concatenating a class of MSCR codes and scalar linear codes. We give a repair
procedure to repair the -MSCR codes in the event of two node failures
and calculate the repair bandwidth for the same. We characterize the increase
in repair bandwidth incurred by the method in comparison with the optimal
repair bandwidth given by the cut-set bound. Finally, we show the
subpacketization level of -MSCR codes scales logarithmically in the
number of nodes.Comment: 14 pages, Keywords: Cooperative repair, MSCR Codes, Subpacketizatio
Rack-aware minimum-storage regenerating codes with optimal access
We derive a lower bound on the amount of information accessed to repair
failed nodes within a single rack from any number of helper racks in the
rack-aware storage model that allows collective information processing in the
nodes that share the same rack. Furthermore, we construct a family of
rack-aware minimum-storage regenerating (MSR) codes with the property that the
number of symbols accessed for repairing a single failed node attains the bound
with equality for all admissible parameters. Constructions of rack-aware
optimal-access MSR codes were only known for limited parameters. We also
present a family of Reed-Solomon (RS) codes that only require accessing a
relatively small number of symbols to repair multiple failed nodes in a single
rack. In particular, for certain code parameters, the RS construction attains
the bound on the access complexity with equality and thus has optimal access
When and By How Much Can Helper Node Selection Improve Regenerating Codes?
Regenerating codes (RCs) can significantly reduce the repair-bandwidth of
distributed storage networks. Initially, the analysis of RCs was based on the
assumption that during the repair process, the newcomer does not distinguish
(among all surviving nodes) which nodes to access, i.e., the newcomer is
oblivious to the set of helpers being used. Such a scheme is termed the blind
repair (BR) scheme. Nonetheless, it is intuitive in practice that the newcomer
should choose to access only those "good" helpers. In this paper, a new
characterization of the effect of choosing the helper nodes in terms of the
storage-bandwidth tradeoff is given. Specifically, answers to the following
fundamental questions are given: Under what conditions does proactively
choosing the helper nodes improve the storage-bandwidth tradeoff? Can this
improvement be analytically quantified?
This paper answers the former question by providing a necessary and
sufficient condition under which optimally choosing good helpers strictly
improves the storage-bandwidth tradeoff. To answer the latter question, a
low-complexity helper selection solution, termed the family repair (FR) scheme,
is proposed and the corresponding storage/repair-bandwidth curve is
characterized. For example, consider a distributed storage network with 60
total number of nodes and the network is resilient against 50 node failures. If
the number of helper nodes is 10, then the FR scheme and its variant
demonstrate 27% reduction in the repair-bandwidth when compared to the BR
solution. This paper also proves that under some design parameters, the FR
scheme is indeed optimal among all helper selection schemes. An explicit
construction of an exact-repair code is also proposed that can achieve the
minimum-bandwidth-regenerating point of the FR scheme. The new exact-repair
code can be viewed as a generalization of the existing fractional repetition
code.Comment: 35 pages, 10 figures, submitted to IEEE Transactions on Information
Theory on September 04, 201
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