110 research outputs found
Cooperative Local Repair in Distributed Storage
Erasure-correcting codes, that support local repair of codeword symbols, have
attracted substantial attention recently for their application in distributed
storage systems. This paper investigates a generalization of the usual locally
repairable codes. In particular, this paper studies a class of codes with the
following property: any small set of codeword symbols can be reconstructed
(repaired) from a small number of other symbols. This is referred to as
cooperative local repair. The main contribution of this paper is bounds on the
trade-off of the minimum distance and the dimension of such codes, as well as
explicit constructions of families of codes that enable cooperative local
repair. Some other results regarding cooperative local repair are also
presented, including an analysis for the well-known Hadamard/Simplex codes.Comment: Fixed some minor issues in Theorem 1, EURASIP Journal on Advances in
Signal Processing, December 201
Access vs. Bandwidth in Codes for Storage
Maximum distance separable (MDS) codes are widely used in storage systems to
protect against disk (node) failures. A node is said to have capacity over
some field , if it can store that amount of symbols of the field.
An MDS code uses nodes of capacity to store information
nodes. The MDS property guarantees the resiliency to any node failures.
An \emph{optimal bandwidth} (resp. \emph{optimal access}) MDS code communicates
(resp. accesses) the minimum amount of data during the repair process of a
single failed node. It was shown that this amount equals a fraction of
of data stored in each node. In previous optimal bandwidth
constructions, scaled polynomially with in codes with asymptotic rate
. Moreover, in constructions with a constant number of parities, i.e. rate
approaches 1, is scaled exponentially w.r.t. . In this paper, we focus
on the later case of constant number of parities , and ask the following
question: Given the capacity of a node what is the largest number of
information disks in an optimal bandwidth (resp. access) MDS
code. We give an upper bound for the general case, and two tight bounds in the
special cases of two important families of codes. Moreover, the bounds show
that in some cases optimal-bandwidth code has larger than optimal-access
code, and therefore these two measures are not equivalent.Comment: This paper was presented in part at the IEEE International Symposium
on Information Theory (ISIT 2012). submitted to IEEE transactions on
information theor
High-Rate Regenerating Codes Through Layering
In this paper, we provide explicit constructions for a class of exact-repair
regenerating codes that possess a layered structure. These regenerating codes
correspond to interior points on the storage-repair-bandwidth tradeoff, and
compare very well in comparison to scheme that employs space-sharing between
MSR and MBR codes. For the parameter set with , we
construct a class of codes with an auxiliary parameter , referred to as
canonical codes. With in the range , these codes operate in
the region between the MSR point and the MBR point, and perform significantly
better than the space-sharing line. They only require a field size greater than
. For the case of , canonical codes can also be shown to
achieve an interior point on the line-segment joining the MSR point and the
next point of slope-discontinuity on the storage-repair-bandwidth tradeoff.
Thus we establish the existence of exact-repair codes on a point other than the
MSR and the MBR point on the storage-repair-bandwidth tradeoff. We also
construct layered regenerating codes for general parameter set ,
which we refer to as non-canonical codes. These codes also perform
significantly better than the space-sharing line, though they require a
significantly higher field size. All the codes constructed in this paper are
high-rate, can repair multiple node-failures and do not require any computation
at the helper nodes. We also construct optimal codes with locality in which the
local codes are layered regenerating codes.Comment: 20 pages, 9 figure
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