560 research outputs found
Repairable Block Failure Resilient Codes
In large scale distributed storage systems (DSS) deployed in cloud computing,
correlated failures resulting in simultaneous failure (or, unavailability) of
blocks of nodes are common. In such scenarios, the stored data or a content of
a failed node can only be reconstructed from the available live nodes belonging
to available blocks. To analyze the resilience of the system against such block
failures, this work introduces the framework of Block Failure Resilient (BFR)
codes, wherein the data (e.g., file in DSS) can be decoded by reading out from
a same number of codeword symbols (nodes) from each available blocks of the
underlying codeword. Further, repairable BFR codes are introduced, wherein any
codeword symbol in a failed block can be repaired by contacting to remaining
blocks in the system. Motivated from regenerating codes, file size bounds for
repairable BFR codes are derived, trade-off between per node storage and repair
bandwidth is analyzed, and BFR-MSR and BFR-MBR points are derived. Explicit
codes achieving these two operating points for a wide set of parameters are
constructed by utilizing combinatorial designs, wherein the codewords of the
underlying outer codes are distributed to BFR codeword symbols according to
projective planes
Distributed Storage Systems based on Equidistant Subspace Codes
Distributed storage systems based on equidistant constant dimension codes are
presented. These equidistant codes are based on the Pl\"{u}cker embedding,
which is essential in the repair and the reconstruction algorithms. These
systems posses several useful properties such as high failure resilience,
minimum bandwidth, low storage, simple algebraic repair and reconstruction
algorithms, good locality, and compatibility with small fields
Repairable Replication-based Storage Systems Using Resolvable Designs
We consider the design of regenerating codes for distributed storage systems
at the minimum bandwidth regeneration (MBR) point. The codes allow for a repair
process that is exact and uncoded, but table-based. These codes were introduced
in prior work and consist of an outer MDS code followed by an inner fractional
repetition (FR) code where copies of the coded symbols are placed on the
storage nodes. The main challenge in this domain is the design of the inner FR
code.
In our work, we consider generalizations of FR codes, by establishing their
connection with a family of combinatorial structures known as resolvable
designs. Our constructions based on affine geometries, Hadamard designs and
mutually orthogonal Latin squares allow the design of systems where a new node
can be exactly regenerated by downloading packets from a subset
of the surviving nodes (prior work only considered the case of ).
Our techniques allow the design of systems over a large range of parameters.
Specifically, the repetition degree of a symbol, which dictates the resilience
of the system can be varied over a large range in a simple manner. Moreover,
the actual table needed for the repair can also be implemented in a rather
straightforward way. Furthermore, we answer an open question posed in prior
work by demonstrating the existence of codes with parameters that are not
covered by Steiner systems
Replication based storage systems with local repair
We consider the design of regenerating codes for distributed storage systems
that enjoy the property of local, exact and uncoded repair, i.e., (a) upon
failure, a node can be regenerated by simply downloading packets from the
surviving nodes and (b) the number of surviving nodes contacted is strictly
smaller than the number of nodes that need to be contacted for reconstructing
the stored file.
Our codes consist of an outer MDS code and an inner fractional repetition
code that specifies the placement of the encoded symbols on the storage nodes.
For our class of codes, we identify the tradeoff between the local repair
property and the minimum distance. We present codes based on graphs of high
girth, affine resolvable designs and projective planes that meet the minimum
distance bound for specific choices of file sizes
Optimal Locally Repairable and Secure Codes for Distributed Storage Systems
This paper aims to go beyond resilience into the study of security and
local-repairability for distributed storage systems (DSS). Security and
local-repairability are both important as features of an efficient storage
system, and this paper aims to understand the trade-offs between resilience,
security, and local-repairability in these systems. In particular, this paper
first investigates security in the presence of colluding eavesdroppers, where
eavesdroppers are assumed to work together in decoding stored information.
Second, the paper focuses on coding schemes that enable optimal local repairs.
It further brings these two concepts together, to develop locally repairable
coding schemes for DSS that are secure against eavesdroppers.
The main results of this paper include: a. An improved bound on the secrecy
capacity for minimum storage regenerating codes, b. secure coding schemes that
achieve the bound for some special cases, c. a new bound on minimum distance
for locally repairable codes, d. code construction for locally repairable codes
that attain the minimum distance bound, and e. repair-bandwidth-efficient
locally repairable codes with and without security constraints.Comment: Submitted to IEEE Transactions on Information Theor
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