1,709 research outputs found
Exact Regeneration Codes for Distributed Storage Repair Using Interference Alignment
The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes
has recently motivated a new class of codes, called Regenerating Codes, that
optimally trade off storage cost for repair bandwidth. On one end of this
spectrum of Regenerating Codes are Minimum Storage Regenerating (MSR) codes
that can match the minimum storage cost of MDS codes while also significantly
reducing repair bandwidth. In this paper, we describe Exact-MSR codes which
allow for any failed nodes (whether they are systematic or parity nodes) to be
regenerated exactly rather than only functionally or information-equivalently.
We show that Exact-MSR codes come with no loss of optimality with respect to
random-network-coding based MSR codes (matching the cutset-based lower bound on
repair bandwidth) for the cases of: (a) k/n <= 1/2; and (b) k <= 3. Our
constructive approach is based on interference alignment techniques, and,
unlike the previous class of random-network-coding based approaches, we provide
explicit and deterministic coding schemes that require a finite-field size of
at most 2(n-k).Comment: to be submitted to IEEE Transactions on Information Theor
On the Existence of Optimal Exact-Repair MDS Codes for Distributed Storage
The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes
has recently motivated a new class of codes, called Regenerating Codes, that
optimally trade off storage cost for repair bandwidth. In this paper, we
address bandwidth-optimal (n,k,d) Exact-Repair MDS codes, which allow for any
failed node to be repaired exactly with access to arbitrary d survivor nodes,
where k<=d<=n-1. We show the existence of Exact-Repair MDS codes that achieve
minimum repair bandwidth (matching the cutset lower bound) for arbitrary
admissible (n,k,d), i.e., k<n and k<=d<=n-1. Our approach is based on
interference alignment techniques and uses vector linear codes which allow to
split symbols into arbitrarily small subsymbols.Comment: 20 pages, 6 figure
Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions
Regenerating codes are a class of recently developed codes for distributed
storage that, like Reed-Solomon codes, permit data recovery from any arbitrary
k of n nodes. However regenerating codes possess in addition, the ability to
repair a failed node by connecting to any arbitrary d nodes and downloading an
amount of data that is typically far less than the size of the data file. This
amount of download is termed the repair bandwidth. Minimum storage regenerating
(MSR) codes are a subclass of regenerating codes that require the least amount
of network storage; every such code is a maximum distance separable (MDS) code.
Further, when a replacement node stores data identical to that in the failed
node, the repair is termed as exact.
The four principal results of the paper are (a) the explicit construction of
a class of MDS codes for d = n-1 >= 2k-1 termed the MISER code, that achieves
the cut-set bound on the repair bandwidth for the exact-repair of systematic
nodes, (b) proof of the necessity of interference alignment in exact-repair MSR
codes, (c) a proof showing the impossibility of constructing linear,
exact-repair MSR codes for d < 2k-3 in the absence of symbol extension, and (d)
the construction, also explicit, of MSR codes for d = k+1. Interference
alignment (IA) is a theme that runs throughout the paper: the MISER code is
built on the principles of IA and IA is also a crucial component to the
non-existence proof for d < 2k-3. To the best of our knowledge, the
constructions presented in this paper are the first, explicit constructions of
regenerating codes that achieve the cut-set bound.Comment: 38 pages, 12 figures, submitted to the IEEE Transactions on
Information Theory;v3 - The title has been modified to better reflect the
contributions of the submission. The paper is extensively revised with
several carefully constructed figures and example
Distributed Data Storage with Minimum Storage Regenerating Codes - Exact and Functional Repair are Asymptotically Equally Efficient
We consider a set up where a file of size M is stored in n distributed
storage nodes, using an (n,k) minimum storage regenerating (MSR) code, i.e., a
maximum distance separable (MDS) code that also allows efficient exact-repair
of any failed node. The problem of interest in this paper is to minimize the
repair bandwidth B for exact regeneration of a single failed node, i.e., the
minimum data to be downloaded by a new node to replace the failed node by its
exact replica. Previous work has shown that a bandwidth of B=[M(n-1)]/[k(n-k)]
is necessary and sufficient for functional (not exact) regeneration. It has
also been shown that if k < = max(n/2, 3), then there is no extra cost of exact
regeneration over functional regeneration. The practically relevant setting of
low-redundancy, i.e., k/n>1/2 remains open for k>3 and it has been shown that
there is an extra bandwidth cost for exact repair over functional repair in
this case. In this work, we adopt into the distributed storage context an
asymptotically optimal interference alignment scheme previously proposed by
Cadambe and Jafar for large wireless interference networks. With this scheme we
solve the problem of repair bandwidth minimization for (n,k) exact-MSR codes
for all (n,k) values including the previously open case of k > \max(n/2,3). Our
main result is that, for any (n,k), and sufficiently large file sizes, there is
no extra cost of exact regeneration over functional regeneration in terms of
the repair bandwidth per bit of regenerated data. More precisely, we show that
in the limit as M approaches infinity, the ratio B/M = (n-1)/(k(n-k))$
Exact Optimized-cost Repair in Multi-hop Distributed Storage Networks
The problem of exact repair of a failed node in multi-hop networked
distributed storage systems is considered. Contrary to the most of the current
studies which model the repair process by the direct links from surviving nodes
to the new node, the repair is modeled by considering the multi-hop network
structure, and taking into account that there might not exist direct links from
all the surviving nodes to the new node. In the repair problem of these
systems, surviving nodes may cooperate to transmit the repair traffic to the
new node. In this setting, we define the total number of packets transmitted
between nodes as repair-cost. A lower bound of the repaircost can thus be found
by cut-set bound analysis. In this paper, we show that the lower bound of the
repair-cost is achievable for the exact repair of MDS codes in tandem and grid
networks, thus resulting in the minimum-cost exact MDS codes. Further, two
suboptimal (achievable) bounds for the large scale grid networks are proposed.Comment: (To appear in ICC 2014
A Construction of Systematic MDS Codes with Minimum Repair Bandwidth
In a distributed storage system based on erasure coding, an important problem
is the \emph{repair problem}: If a node storing a coded piece fails, in order
to maintain the same level of reliability, we need to create a new encoded
piece and store it at a new node. This paper presents a construction of
systematic -MDS codes for that achieves the minimum repair
bandwidth when repairing from nodes.Comment: Submitted to IEEE Transactions on Information Theory on August 14,
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A Framework of Constructions of Minimal Storage Regenerating Codes with the Optimal Access/Update Property
In this paper, we present a generic framework for constructing systematic
minimum storage regenerating codes with two parity nodes based on the invariant
subspace technique. Codes constructed in our framework not only contain some
best known codes as special cases, but also include some new codes with key
properties such as the optimal access property and the optimal update property.
In particular, for a given storage capacity of an individual node, one of the
new codes has the largest number of systematic nodes and two of the new codes
have the largest number of systematic nodes with the optimal update property.Comment: Accepted for publication in IEEE Transactions on Information Theor
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