3,143 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
An Improved Outer Bound on the Storage-Repair-Bandwidth Tradeoff of Exact-Repair Regenerating Codes
In this paper we establish an improved outer bound on the
storage-repair-bandwidth tradeoff of regenerating codes under exact repair. The
result shows that in particular, it is not possible to construct exact-repair
regenerating codes that asymptotically achieve the tradeoff that holds for
functional repair. While this had been shown earlier by Tian for the special
case of the present result holds for general . The
new outer bound is obtained by building on the framework established earlier by
Shah et al.Comment: 14 page
Multilevel Diversity Coding with Secure Regeneration: Separate Coding Achieves the MBR Point
The problem of multilevel diversity coding with secure regeneration (MDC-SR)
is considered, which includes the problems of multilevel diversity coding with
regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two
outer bounds are established, showing that separate coding of different
messages using the respective SRCs can achieve the
minimum-bandwidth-regeneration (MBR) point of the achievable normalized
storage-capacity repair-bandwidth tradeoff regions for the general MDC-SR
problem. The core of the new converse results is an exchange lemma, which can
be established using Han's subset inequality
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