8,172 research outputs found
Node Repair for Distributed Storage Systems over Fading Channels
Distributed storage systems and associated storage codes can efficiently
store a large amount of data while ensuring that data is retrievable in case of
node failure. The study of such systems, particularly the design of storage
codes over finite fields, assumes that the physical channel through which the
nodes communicate is error-free. This is not always the case, for example, in a
wireless storage system.
We study the probability that a subpacket is repaired incorrectly during node
repair in a distributed storage system, in which the nodes communicate over an
AWGN or Rayleigh fading channels. The asymptotic probability (as SNR increases)
that a node is repaired incorrectly is shown to be completely determined by the
repair locality of the DSS and the symbol error rate of the wireless channel.
Lastly, we propose some design criteria for physical layer coding in this
scenario, and use it to compute optimally rotated QAM constellations for use in
wireless distributed storage systems.Comment: To appear in ISITA 201
Reliability of Erasure Coded Storage Systems: A Geometric Approach
We consider the probability of data loss, or equivalently, the reliability
function for an erasure coded distributed data storage system under worst case
conditions. Data loss in an erasure coded system depends on probability
distributions for the disk repair duration and the disk failure duration. In
previous works, the data loss probability of such systems has been studied
under the assumption of exponentially distributed disk failure and disk repair
durations, using well-known analytic methods from the theory of Markov
processes. These methods lead to an estimate of the integral of the reliability
function.
Here, we address the problem of directly calculating the data loss
probability for general repair and failure duration distributions. A closed
limiting form is developed for the probability of data loss and it is shown
that the probability of the event that a repair duration exceeds a failure
duration is sufficient for characterizing the data loss probability.
For the case of constant repair duration, we develop an expression for the
conditional data loss probability given the number of failures experienced by a
each node in a given time window. We do so by developing a geometric approach
that relies on the computation of volumes of a family of polytopes that are
related to the code. An exact calculation is provided and an upper bound on the
data loss probability is obtained by posing the problem as a set avoidance
problem. Theoretical calculations are compared to simulation results.Comment: 28 pages. 8 figures. Presented in part at IEEE International
Conference on BigData 2013, Santa Clara, CA, Oct. 2013 and to be presented in
part at 2014 IEEE Information Theory Workshop, Tasmania, Australia, Nov.
2014. New analysis added May 2015. Further Update Aug. 201
Estimating the Probability of a Rare Event Over a Finite Time Horizon
We study an approximation for the zero-variance change of measure to estimate the probability of a rare event in a continuous-time Markov chain. The rare event occurs when the chain reaches a given set of states before some fixed time limit. The jump rates of the chain are expressed as functions of a rarity parameter in a way that the probability of the rare event goes to zero when the rarity parameter goes to zero, and the behavior of our estimators is studied in this asymptotic regime. After giving a general expression for the zero-variance change of measure in this situation, we develop an approximation of it via a power series and show that this approximation provides a bounded relative error when the rarity parameter goes to zero. We illustrate the performance of our approximation on small numerical examples of highly reliableMarkovian systems. We compare it to a previously proposed heuristic that combines forcing with balanced failure biaising. We also exhibit the exact zero-variance change of measure for these examples and compare it with these two approximations
Combinatorial Alphabet-Dependent Bounds for Locally Recoverable Codes
Locally recoverable (LRC) codes have recently been a focus point of research
in coding theory due to their theoretical appeal and applications in
distributed storage systems. In an LRC code, any erased symbol of a codeword
can be recovered by accessing only a small number of other symbols. For LRC
codes over a small alphabet (such as binary), the optimal rate-distance
trade-off is unknown. We present several new combinatorial bounds on LRC codes
including the locality-aware sphere packing and Plotkin bounds. We also develop
an approach to linear programming (LP) bounds on LRC codes. The resulting LP
bound gives better estimates in examples than the other upper bounds known in
the literature. Further, we provide the tightest known upper bound on the rate
of linear LRC codes with a given relative distance, an improvement over the
previous best known bounds.Comment: To appear in IEEE Transactions on Information Theor
Techniques for the Fast Simulation of Models of Highly dependable Systems
With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system
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