57 research outputs found
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
Error Resilience in Distributed Storage via Rank-Metric Codes
This paper presents a novel coding scheme for distributed storage systems
containing nodes with adversarial errors. The key challenge in such systems is
the propagation of erroneous data from a single corrupted node to the rest of
the system during a node repair process. This paper presents a concatenated
coding scheme which is based on two types of codes: maximum rank distance (MRD)
code as an outer code and optimal repair maximal distance separable (MDS) array
code as an inner code. Given this, two different types of adversarial errors
are considered: the first type considers an adversary that can replace the
content of an affected node only once; while the second attack-type considers
an adversary that can pollute data an unbounded number of times. This paper
proves that the proposed coding scheme attains a suitable upper bound on
resilience capacity for the first type of error. Further, the paper presents
mechanisms that combine this code with subspace signatures to achieve error
resilience for the second type of errors. Finally, the paper concludes by
presenting a construction based on MRD codes for optimal locally repairable
scalar codes that can tolerate adversarial errors
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