7,289 research outputs found
Storage codes -- coding rate and repair locality
The {\em repair locality} of a distributed storage code is the maximum number
of nodes that ever needs to be contacted during the repair of a failed node.
Having small repair locality is desirable, since it is proportional to the
number of disk accesses during repair. However, recent publications show that
small repair locality comes with a penalty in terms of code distance or storage
overhead if exact repair is required.
Here, we first review some of the main results on storage codes under various
repair regimes and discuss the recent work on possible
(information-theoretical) trade-offs between repair locality and other code
parameters like storage overhead and code distance, under the exact repair
regime.
Then we present some new information theoretical lower bounds on the storage
overhead as a function of the repair locality, valid for all common coding and
repair models. In particular, we show that if each of the nodes in a
distributed storage system has storage capacity \ga and if, at any time, a
failed node can be {\em functionally} repaired by contacting {\em some} set of
nodes (which may depend on the actual state of the system) and downloading
an amount \gb of data from each, then in the extreme cases where \ga=\gb or
\ga = r\gb, the maximal coding rate is at most or 1/2, respectively
(that is, the excess storage overhead is at least or 1, respectively).Comment: Accepted for publication in ICNC'13, San Diego, US
Quantization of the Reissner-Nordstr\"{o}m Black Hole
The Reissner--Nordstr\"{o}m family of solutions can be understood to arise
from the spherically symmetric sector of a nonlinear SO(2,1)/SO(1,1) sigma
model coupled to three dimensional Euclidean gravity. In this context a group
theoretical quantization is performed. We identify the observables of the
theory and calculate their spectra.Comment: 8 pages, Late
Association schemes from the action of fixing a nonsingular conic in PG(2,q)
The group has an embedding into such that it acts as
the group fixing a nonsingular conic in . This action affords a
coherent configuration on the set of non-tangent lines of the
conic. We show that the relations can be described by using the cross-ratio.
Our results imply that the restrictions and to the sets
of secant lines and to the set of exterior lines,
respectively, are both association schemes; moreover, we show that the elliptic
scheme is pseudocyclic.
We further show that the coherent configuration with even allow
certain fusions. These provide a 4-class fusion of the hyperbolic scheme
, and 3-class fusions and 2-class fusions (strongly regular graphs)
of both schemes and $R_{-}(q^2). The fusion results for the
hyperbolic case are known, but our approach here as well as our results in the
elliptic case are new.Comment: 33 page
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