3,684 research outputs found
Cooperative Data Exchange based on MDS Codes
The cooperative data exchange problem is studied for the fully connected
network. In this problem, each node initially only possesses a subset of the
packets making up the file. Nodes make broadcast transmissions that are
received by all other nodes. The goal is for each node to recover the full
file. In this paper, we present a polynomial-time deterministic algorithm to
compute the optimal (i.e., minimal) number of required broadcast transmissions
and to determine the precise transmissions to be made by the nodes. A
particular feature of our approach is that {\it each} of the
transmissions is a linear combination of {\it exactly} packets, and we
show how to optimally choose the value of We also show how the
coefficients of these linear combinations can be chosen by leveraging a
connection to Maximum Distance Separable (MDS) codes. Moreover, we show that
our method can be used to solve cooperative data exchange problems with
weighted cost as well as the so-called successive local omniscience problem.Comment: 21 pages, 1 figur
On the Existence of MDS Codes Over Small Fields With Constrained Generator Matrices
We study the existence over small fields of Maximum Distance Separable (MDS)
codes with generator matrices having specified supports (i.e. having specified
locations of zero entries). This problem unifies and simplifies the problems
posed in recent works of Yan and Sprintson (NetCod'13) on weakly secure
cooperative data exchange, of Halbawi et al. (arxiv'13) on distributed
Reed-Solomon codes for simple multiple access networks, and of Dau et al.
(ISIT'13) on MDS codes with balanced and sparse generator matrices. We
conjecture that there exist such MDS codes as long as , if the specified supports of the generator matrices satisfy the so-called
MDS condition, which can be verified in polynomial time. We propose a
combinatorial approach to tackle the conjecture, and prove that the conjecture
holds for a special case when the sets of zero coordinates of rows of the
generator matrix share with each other (pairwise) at most one common element.
Based on our numerical result, the conjecture is also verified for all . Our approach is based on a novel generalization of the well-known Hall's
marriage theorem, which allows (overlapping) multiple representatives instead
of a single representative for each subset.Comment: 8 page
Cooperative Regenerating Codes for Distributed Storage Systems
When there are multiple node failures in a distributed storage system,
regenerating the failed storage nodes individually in a one-by-one manner is
suboptimal as far as repair-bandwidth minimization is concerned. If data
exchange among the newcomers is enabled, we can get a better tradeoff between
repair bandwidth and the storage per node. An explicit and optimal construction
of cooperative regenerating code is illustrated.Comment: 5 pages, 7 figures, to appear in Proc. IEEE ICC, 201
Secure Cooperative Regenerating Codes for Distributed Storage Systems
Regenerating codes enable trading off repair bandwidth for storage in
distributed storage systems (DSS). Due to their distributed nature, these
systems are intrinsically susceptible to attacks, and they may also be subject
to multiple simultaneous node failures. Cooperative regenerating codes allow
bandwidth efficient repair of multiple simultaneous node failures. This paper
analyzes storage systems that employ cooperative regenerating codes that are
robust to (passive) eavesdroppers. The analysis is divided into two parts,
studying both minimum bandwidth and minimum storage cooperative regenerating
scenarios. First, the secrecy capacity for minimum bandwidth cooperative
regenerating codes is characterized. Second, for minimum storage cooperative
regenerating codes, a secure file size upper bound and achievability results
are provided. These results establish the secrecy capacity for the minimum
storage scenario for certain special cases. In all scenarios, the achievability
results correspond to exact repair, and secure file size upper bounds are
obtained using min-cut analyses over a suitable secrecy graph representation of
DSS. The main achievability argument is based on an appropriate pre-coding of
the data to eliminate the information leakage to the eavesdropper
CORE: Augmenting Regenerating-Coding-Based Recovery for Single and Concurrent Failures in Distributed Storage Systems
Data availability is critical in distributed storage systems, especially when
node failures are prevalent in real life. A key requirement is to minimize the
amount of data transferred among nodes when recovering the lost or unavailable
data of failed nodes. This paper explores recovery solutions based on
regenerating codes, which are shown to provide fault-tolerant storage and
minimum recovery bandwidth. Existing optimal regenerating codes are designed
for single node failures. We build a system called CORE, which augments
existing optimal regenerating codes to support a general number of failures
including single and concurrent failures. We theoretically show that CORE
achieves the minimum possible recovery bandwidth for most cases. We implement
CORE and evaluate our prototype atop a Hadoop HDFS cluster testbed with up to
20 storage nodes. We demonstrate that our CORE prototype conforms to our
theoretical findings and achieves recovery bandwidth saving when compared to
the conventional recovery approach based on erasure codes.Comment: 25 page
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