56,233 research outputs found
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
Update-Efficient Regenerating Codes with Minimum Per-Node Storage
Regenerating codes provide an efficient way to recover data at failed nodes
in distributed storage systems. It has been shown that regenerating codes can
be designed to minimize the per-node storage (called MSR) or minimize the
communication overhead for regeneration (called MBR). In this work, we propose
a new encoding scheme for [n,d] error- correcting MSR codes that generalizes
our earlier work on error-correcting regenerating codes. We show that by
choosing a suitable diagonal matrix, any generator matrix of the [n,{\alpha}]
Reed-Solomon (RS) code can be integrated into the encoding matrix. Hence, MSR
codes with the least update complexity can be found. An efficient decoding
scheme is also proposed that utilizes the [n,{\alpha}] RS code to perform data
reconstruction. The proposed decoding scheme has better error correction
capability and incurs the least number of node accesses when errors are
present.Comment: Submitted to IEEE ISIT 201
Explicit MDS Codes for Optimal Repair Bandwidth
MDS codes are erasure-correcting codes that can correct the maximum number of
erasures for a given number of redundancy or parity symbols. If an MDS code has
parities and no more than erasures occur, then by transmitting all the
remaining data in the code, the original information can be recovered. However,
it was shown that in order to recover a single symbol erasure, only a fraction
of of the information needs to be transmitted. This fraction is called
the repair bandwidth (fraction). Explicit code constructions were given in
previous works. If we view each symbol in the code as a vector or a column over
some field, then the code forms a 2D array and such codes are especially widely
used in storage systems. In this paper, we address the following question:
given the length of the column , number of parities , can we construct
high-rate MDS array codes with optimal repair bandwidth of , whose code
length is as long as possible? In this paper, we give code constructions such
that the code length is .Comment: 17 page
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