15,552 research outputs found
Large Deviations Behavior of the Logarithmic Error Probability of Random Codes
This work studies the deviations of the error exponent of the constant composition code ensemble around its expectation, known as the error exponent of the typical random code (TRC). In particular, it is shown that the probability of randomly drawing a codebook whose error exponent is smaller than the TRC exponent is exponentially small; upper and lower bounds for this exponent are given, which coincide in some cases. In addition, the probability of randomly drawing a codebook whose error exponent is larger than the TRC exponent is shown to be double–exponentially small; upper and lower bounds to the double–exponential exponent are given. The results suggest that codebooks whose error exponent is larger than the error exponent of the TRC are extremely rare. The key ingredient in the proofs is a new large deviations result of type class enumerators with dependent variables
Emerging criticality in the disordered three-color Ashkin-Teller model
We study the effects of quenched disorder on the first-order phase transition
in the two-dimensional three-color Ashkin-Teller model by means of large-scale
Monte Carlo simulations. We demonstrate that the first-order phase transition
is rounded by the disorder and turns into a continuous one. Using a careful
finite-size-scaling analysis, we provide strong evidence for the emerging
critical behavior of the disordered Ashkin-Teller model to be in the clean
two-dimensional Ising universality class, accompanied by universal logarithmic
corrections. This agrees with perturbative renormalization-group predictions by
Cardy. As a byproduct, we also provide support for the strong-universality
scenario for the critical behavior of the two-dimensional disordered Ising
model. We discuss consequences of our results for the classification of
disordered phase transitions as well as generalizations to other systems.Comment: 18 pages, 18 eps figures included, final version as publishe
Concentration of Measure Inequalities in Information Theory, Communications and Coding (Second Edition)
During the last two decades, concentration inequalities have been the subject
of exciting developments in various areas, including convex geometry,
functional analysis, statistical physics, high-dimensional statistics, pure and
applied probability theory, information theory, theoretical computer science,
and learning theory. This monograph focuses on some of the key modern
mathematical tools that are used for the derivation of concentration
inequalities, on their links to information theory, and on their various
applications to communications and coding. In addition to being a survey, this
monograph also includes various new recent results derived by the authors. The
first part of the monograph introduces classical concentration inequalities for
martingales, as well as some recent refinements and extensions. The power and
versatility of the martingale approach is exemplified in the context of codes
defined on graphs and iterative decoding algorithms, as well as codes for
wireless communication. The second part of the monograph introduces the entropy
method, an information-theoretic technique for deriving concentration
inequalities. The basic ingredients of the entropy method are discussed first
in the context of logarithmic Sobolev inequalities, which underlie the
so-called functional approach to concentration of measure, and then from a
complementary information-theoretic viewpoint based on transportation-cost
inequalities and probability in metric spaces. Some representative results on
concentration for dependent random variables are briefly summarized, with
emphasis on their connections to the entropy method. Finally, we discuss
several applications of the entropy method to problems in communications and
coding, including strong converses, empirical distributions of good channel
codes, and an information-theoretic converse for concentration of measure.Comment: Foundations and Trends in Communications and Information Theory, vol.
10, no 1-2, pp. 1-248, 2013. Second edition was published in October 2014.
ISBN to printed book: 978-1-60198-906-
First-Passage Time and Large-Deviation Analysis for Erasure Channels with Memory
This article considers the performance of digital communication systems
transmitting messages over finite-state erasure channels with memory.
Information bits are protected from channel erasures using error-correcting
codes; successful receptions of codewords are acknowledged at the source
through instantaneous feedback. The primary focus of this research is on
delay-sensitive applications, codes with finite block lengths and, necessarily,
non-vanishing probabilities of decoding failure. The contribution of this
article is twofold. A methodology to compute the distribution of the time
required to empty a buffer is introduced. Based on this distribution, the mean
hitting time to an empty queue and delay-violation probabilities for specific
thresholds can be computed explicitly. The proposed techniques apply to
situations where the transmit buffer contains a predetermined number of
information bits at the onset of the data transfer. Furthermore, as additional
performance criteria, large deviation principles are obtained for the empirical
mean service time and the average packet-transmission time associated with the
communication process. This rigorous framework yields a pragmatic methodology
to select code rate and block length for the communication unit as functions of
the service requirements. Examples motivated by practical systems are provided
to further illustrate the applicability of these techniques.Comment: To appear in IEEE Transactions on Information Theor
Why is order flow so persistent?
Order flow in equity markets is remarkably persistent in the sense that order
signs (to buy or sell) are positively autocorrelated out to time lags of tens
of thousands of orders, corresponding to many days. Two possible explanations
are herding, corresponding to positive correlation in the behavior of different
investors, or order splitting, corresponding to positive autocorrelation in the
behavior of single investors. We investigate this using order flow data from
the London Stock Exchange for which we have membership identifiers. By
formulating models for herding and order splitting, as well as models for
brokerage choice, we are able to overcome the distortion introduced by
brokerage. On timescales of less than a few hours the persistence of order flow
is overwhelmingly due to splitting rather than herding. We also study the
properties of brokerage order flow and show that it is remarkably consistent
both cross-sectionally and longitudinally.Comment: 42 pages, 15 figure
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