5,570 research outputs found
Non-Analyticity and the van der Waals Limit
We study the analyticity properties of the free energy f_\ga(m) of the Kac
model at points of first order phase transition, in the van der Waals limit
\ga\searrow 0. We show that there exists an inverse temperature and
\ga_0>0 such that for all and for all \ga\in(0,\ga_0),
f_\ga(m) has no analytic continuation along the path (
denotes spontaneous magnetization). The proof consists in studying high order
derivatives of the pressure p_\ga(h), which is related to the free energy
f_\ga(m) by a Legendre transform
HITECH Revisited
Assesses the 2009 Health Information Technology for Economic and Clinical Health Act, which offers incentives to adopt and meaningfully use electronic health records. Recommendations include revised criteria, incremental approaches, and targeted policies
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
Geochemical and lithium isotope characterization of Ogallala aquifer and Permian Basin carbonate reservoir waters at an enhanced oil recovery site, northwest Texas, USA
Geochemical and lithium isotope compositions (δ7Li) of Permian Basin produced waters and groundwater from overlying aquifers at an enhanced oil recovery (EOR) site in Gaines County, northwest Texas were determined to evaluate the effects of brine-groundwater-rock interactions, identify sources of dissolved solids, and characterize fluid migration and mixing processes. δ7Li values for produced waters from dolostones of the Permian Basin San Andres Formation ranged from +11 to +16 per mil (‰) and fall within the range of formation waters from Gulf of Mexico and Appalachian basin oil and gas reservoir rocks. The chemical composition and TDS content (800 to 2,200 mg L-1) of water from five Tertiary Ogallala Formation groundwater wells in the study area is comparable to other groundwaters from the Southern High Plains aquifer. Groundwaters from the Triassic Dockum Group Santa Rosa (δ7Li range of +21 to +23) are isotopically distinct from waters from the San Andres and Ogallala Formations. In addition to tracking groundwater-brine mixing and water-rock interaction, temporal changes in the δ7Li composition of deep groundwater in the study area has potential use in the early detection of upward or injection-induced brine migration, prior to its incursion into the sensitive overlying Ogallala aquifer
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
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