3,432 research outputs found
A Rate-Distortion Exponent Approach to Multiple Decoding Attempts for Reed-Solomon Codes
Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes
have recently attracted new attention. Choosing decoding candidates based on
rate-distortion (R-D) theory, as proposed previously by the authors, currently
provides the best performance-versus-complexity trade-off. In this paper, an
analysis based on the rate-distortion exponent (RDE) is used to directly
minimize the exponential decay rate of the error probability. This enables
rigorous bounds on the error probability for finite-length RS codes and leads
to modest performance gains. As a byproduct, a numerical method is derived that
computes the rate-distortion exponent for independent non-identical sources.
Analytical results are given for errors/erasures decoding.Comment: accepted for presentation at 2010 IEEE International Symposium on
Information Theory (ISIT 2010), Austin TX, US
On Multiple Decoding Attempts for Reed-Solomon Codes: A Rate-Distortion Approach
One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is
based on using multiple trials of a simple RS decoding algorithm in combination
with erasing or flipping a set of symbols or bits in each trial. This paper
presents a framework based on rate-distortion (RD) theory to analyze these
multiple-decoding algorithms. By defining an appropriate distortion measure
between an error pattern and an erasure pattern, the successful decoding
condition, for a single errors-and-erasures decoding trial, becomes equivalent
to distortion being less than a fixed threshold. Finding the best set of
erasure patterns also turns into a covering problem which can be solved
asymptotically by rate-distortion theory. Thus, the proposed approach can be
used to understand the asymptotic performance-versus-complexity trade-off of
multiple errors-and-erasures decoding of RS codes.
This initial result is also extended a few directions. The rate-distortion
exponent (RDE) is computed to give more precise results for moderate
blocklengths. Multiple trials of algebraic soft-decision (ASD) decoding are
analyzed using this framework. Analytical and numerical computations of the RD
and RDE functions are also presented. Finally, simulation results show that
sets of erasure patterns designed using the proposed methods outperform other
algorithms with the same number of decoding trials.Comment: to appear in the IEEE Transactions on Information Theory (Special
Issue on Facets of Coding Theory: from Algorithms to Networks
A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions
Low-density parity-check (LDPC) convolutional codes (or spatially-coupled
codes) were recently shown to approach capacity on the binary erasure channel
(BEC) and binary-input memoryless symmetric channels. The mechanism behind this
spectacular performance is now called threshold saturation via spatial
coupling. This new phenomenon is characterized by the belief-propagation
threshold of the spatially-coupled ensemble increasing to an intrinsic noise
threshold defined by the uncoupled system. In this paper, we present a simple
proof of threshold saturation that applies to a wide class of coupled scalar
recursions. Our approach is based on constructing potential functions for both
the coupled and uncoupled recursions. Our results actually show that the fixed
point of the coupled recursion is essentially determined by the minimum of the
uncoupled potential function and we refer to this phenomenon as Maxwell
saturation. A variety of examples are considered including the
density-evolution equations for: irregular LDPC codes on the BEC, irregular
low-density generator matrix codes on the BEC, a class of generalized LDPC
codes with BCH component codes, the joint iterative decoding of LDPC codes on
intersymbol-interference channels with erasure noise, and the compressed
sensing of random vectors with i.i.d. components.Comment: This article is an extended journal version of arXiv:1204.5703 and
has now been accepted to the IEEE Transactions on Information Theory. This
version adds additional explanation for some details and also corrects a
number of small typo
Abstract cluster expansion with applications to statistical mechanical systems
We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions
Quadripartite continuous-variable entanglement via quadruply concurrent downconversion
We investigate an intra-cavity coupled down-conversion scheme to generate
quadripartite entanglement using concurrently resonant nonlinearities. We
verify that quadripartite entanglement is present in this system by calculating
the output fluctuation spectra and then considering violations of optimized
inequalities of the van Loock-Furusawa type. The entanglement characteristics
both above and below the oscillation threshold are considered. We also present
analytic solutions for the quadrature operators and the van Loock-Furusawa
correlations in the undepleted pump approximation.Comment: 9 pages, 5 figure
Optimizing moxidectin dosing for Strongyloides stercoralis infections: insights from pharmacometric modeling
Moxidectin is a frontrunner drug candidate in the treatment of strongyloidiasis. A dose of 8 mg is recommended to treat this indication, which shows a reasonably good efficacy and tolerability profile. Yet, owing to the unique life cycle of Strongyloides stercoralis (S. stercoralis) that entails internal autoinfection, a curative treatment would be desirable. Population-based pharmacometric modeling that would help to identify an ideal dosing strategy are yet lacking. The aims of this study were to (i) explore the exposure-efficacy response relationship of moxidectin in treating S. stercoralis and (ii) evaluate whether moxidectin treatment outcomes in terms of cure rates at baseline as compared to post-treatment could be optimized. Our pharmacodynamic model suggests high predictive power (area under the concentration time curve-receiver operating characteristic [AUC-ROC] 0.817) in the probability of being cured by linking an exposure metric (i.e., AUC0-24 or maximum concentration [Cmax ]) to baseline infection intensity. Pharmacometric simulations indicate that with a minimum dose of 4 mg a maximum cure rate of ~ 95% is established in the low infection intensity group (larvae per gram [LPG] >/=0.4-1), whereas in the moderate-to-high intensity group (LPG >1) the cure rate plateaus at ~ 87%, following an 8 mg dose. To enhance efficacy further, studies using repeated dosing based on the duration of the autoinfection cycle, for example a two-dose regimen 3 weeks apart should be considered. Simulations revealed similar Cmax in both treatment courses of a two-dose regimen; hence safety should not be a concern. Collectively, our results provide evidence-based guidance for enhanced dosing strategies and should be considered when designing future treatment strategies
Centrifugal force induced by relativistically rotating spheroids and cylinders
Starting from the gravitational potential of a Newtonian spheroidal shell we
discuss electrically charged rotating prolate spheroidal shells in the Maxwell
theory. In particular we consider two confocal charged shells which rotate
oppositely in such a way that there is no magnetic field outside the outer
shell. In the Einstein theory we solve the Ernst equations in the region where
the long prolate spheroids are almost cylindrical; in equatorial regions the
exact Lewis "rotating cylindrical" solution is so derived by a limiting
procedure from a spatially bound system. In the second part we analyze two
cylindrical shells rotating in opposite directions in such a way that the
static Levi-Civita metric is produced outside and no angular momentum flux
escapes to infinity. The rotation of the local inertial frames in flat space
inside the inner cylinder is thus exhibited without any approximation or
interpretational difficulties within this model.
A test particle within the inner cylinder kept at rest with respect to axes
that do not rotate as seen from infinity experiences a centrifugal force.
Although the spacetime there is Minkowskian out to the inner cylinder
nevertheless that space has been induced to rotate, so relative to the local
inertial frame the particle is traversing a circular orbit.Comment: 12 pages, 2 figure
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