1,123 research outputs found
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
Optimal block cosine transform image coding for noisy channels
The two dimensional block transform coding scheme based on the discrete cosine transform was studied extensively for image coding applications. While this scheme has proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. A method is presented for the joint source channel coding optimization of a scheme based on the 2-D block cosine transform when the output of the encoder is to be transmitted via a memoryless design of the quantizers used for encoding the transform coefficients. This algorithm produces a set of locally optimum quantizers and the corresponding binary code assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, an algorithm was used based on the steepest descent method, which under certain convexity conditions on the performance of the channel optimized quantizers, yields the optimal bit allocation. Comprehensive simulation results for the performance of this locally optimum system over noisy channels were obtained and appropriate comparisons against a reference system designed for no channel error were rendered
A Zador-Like Formula for Quantizers Based on Periodic Tilings
We consider Zador's asymptotic formula for the distortion-rate function for a
variable-rate vector quantizer in the high-rate case. This formula involves the
differential entropy of the source, the rate of the quantizer in bits per
sample, and a coefficient G which depends on the geometry of the quantizer but
is independent of the source. We give an explicit formula for G in the case
when the quantizing regions form a periodic tiling of n-dimensional space, in
terms of the volumes and second moments of the Voronoi cells. As an application
we show, extending earlier work of Kashyap and Neuhoff, that even a
variable-rate three-dimensional quantizer based on the ``A15'' structure is
still inferior to a quantizer based on the body-centered cubic lattice. We also
determine the smallest covering radius of such a structure.Comment: 8 page
The Year in Review for Renal Cancer
The treatment of kidney cancer has made some remarkable strides over the last few years. Two regimens received Food and Drug Administration (FDA) approval, multiple biomarkers were reported to show promise, and further enhancement and refinement of the prognostic characteristics occurred. The combinations of anti-angiogenic tyrosine kinase inhibitors with immune checkpoint inhibitors have rapidly become the preferred therapies in the front-line setting of advanced renal cancer
A user's guide for the signal processing software for image and speech compression developed in the Communications and Signal Processing Laboratory (CSPL), version 1
A complete documentation of the software developed in the Communication and Signal Processing Laboratory (CSPL) during the period of July 1985 to March 1986 is provided. Utility programs and subroutines that were developed for a user-friendly image and speech processing environment are described. Additional programs for data compression of image and speech type signals are included. Also, programs for the zero-memory and block transform quantization in the presence of channel noise are described. Finally, several routines for simulating the perfromance of image compression algorithms are included
Constructive spherical codes on layers of flat tori
A new class of spherical codes is constructed by selecting a finite subset of
flat tori from a foliation of the unit sphere S^{2L-1} of R^{2L} and designing
a structured codebook on each torus layer. The resulting spherical code can be
the image of a lattice restricted to a specific hyperbox in R^L in each layer.
Group structure and homogeneity, useful for efficient storage and decoding, are
inherited from the underlying lattice codebook. A systematic method for
constructing such codes are presented and, as an example, the Leech lattice is
used to construct a spherical code in R^{48}. Upper and lower bounds on the
performance, the asymptotic packing density and a method for decoding are
derived.Comment: 9 pages, 5 figures, submitted to IEEE Transactions on Information
Theor
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