3,484 research outputs found
Comments on 'a representation for the symbol error rate using completely monotone functions'
It was shown in the above-titled paper by Rajan and Tepedelenlioglu (see ibid., vol. 59, no. 6, p. 3922-31, June 2013) that the symbol error rate (SER) of an arbitrary multidimensional constellation subject to additive white Gaussian noise is characterized as the product of a completely monotone function with a nonnegative power of signal-to-noise ratio (SNR) under minimum distance detection. In this comment, it is proved that the probability of correct decision of an arbitrary constellation admits a similar representation as well. Based on this fact, it is shown that the stochastic ordering { G α} proposed by the authors as an extension of the existing Laplace transform order to compare the average SERs over two different fading channels actually predicts that the average SERs are equal for any constellation of dimensionality smaller than or equal to 2α. Furthermore, it is noted that there are no positive random variables X1 and X2 such that the proposed stochastic ordering is satisfied in the strict sense, i.e., X1<Gα X2, when α=N/2 for any positive integer N. Additional remarks are noted about the fading scenarios at low SNR and the generalization to additive compound Gaussian noise originally discussed in the subject paper. © 1963-2012 IEEE
12th International Workshop on Termination (WST 2012) : WST 2012, February 19â23, 2012, Obergurgl, Austria / ed. by Georg Moser
This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19â23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto
Estimation of the Rate-Distortion Function
Motivated by questions in lossy data compression and by theoretical
considerations, we examine the problem of estimating the rate-distortion
function of an unknown (not necessarily discrete-valued) source from empirical
data. Our focus is the behavior of the so-called "plug-in" estimator, which is
simply the rate-distortion function of the empirical distribution of the
observed data. Sufficient conditions are given for its consistency, and
examples are provided to demonstrate that in certain cases it fails to converge
to the true rate-distortion function. The analysis of its performance is
complicated by the fact that the rate-distortion function is not continuous in
the source distribution; the underlying mathematical problem is closely related
to the classical problem of establishing the consistency of maximum likelihood
estimators. General consistency results are given for the plug-in estimator
applied to a broad class of sources, including all stationary and ergodic ones.
A more general class of estimation problems is also considered, arising in the
context of lossy data compression when the allowed class of coding
distributions is restricted; analogous results are developed for the plug-in
estimator in that case. Finally, consistency theorems are formulated for
modified (e.g., penalized) versions of the plug-in, and for estimating the
optimal reproduction distribution.Comment: 18 pages, no figures [v2: removed an example with an error; corrected
typos; a shortened version will appear in IEEE Trans. Inform. Theory
Kalikow-type decomposition for multicolor infinite range particle systems
We consider a particle system on with real state space and
interactions of infinite range. Assuming that the rate of change is continuous
we obtain a Kalikow-type decomposition of the infinite range change rates as a
mixture of finite range change rates. Furthermore, if a high noise condition
holds, as an application of this decomposition, we design a feasible perfect
simulation algorithm to sample from the stationary process. Finally, the
perfect simulation scheme allows us to forge an algorithm to obtain an explicit
construction of a coupling attaining Ornstein's -distance for two
ordered Ising probability measures.Comment: Published in at http://dx.doi.org/10.1214/12-AAP882 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The resource theory of informational nonequilibrium in thermodynamics
We review recent work on the foundations of thermodynamics in the light of
quantum information theory. We adopt a resource-theoretic perspective, wherein
thermodynamics is formulated as a theory of what agents can achieve under a
particular restriction, namely, that the only state preparations and
transformations that they can implement for free are those that are thermal at
some fixed temperature. States that are out of thermal equilibrium are the
resources. We consider the special case of this theory wherein all systems have
trivial Hamiltonians (that is, all of their energy levels are degenerate). In
this case, the only free operations are those that add noise to the system (or
implement a reversible evolution) and the only nonequilibrium states are states
of informational nonequilibrium, that is, states that deviate from the
maximally mixed state. The degree of this deviation we call the state's
nonuniformity; it is the resource of interest here, the fuel that is consumed,
for instance, in an erasure operation. We consider the different types of state
conversion: exact and approximate, single-shot and asymptotic, catalytic and
noncatalytic. In each case, we present the necessary and sufficient conditions
for the conversion to be possible for any pair of states, emphasizing a
geometrical representation of the conditions in terms of Lorenz curves. We also
review the problem of quantifying the nonuniformity of a state, in particular
through the use of generalized entropies. Quantum state conversion problems in
this resource theory can be shown to be always reducible to their classical
counterparts, so that there are no inherently quantum-mechanical features
arising in such problems. This body of work also demonstrates that the standard
formulation of the second law of thermodynamics is inadequate as a criterion
for deciding whether or not a given state transition is possible.Comment: 51 pages, 9 figures, Revised Versio
Asymptotics of Discrete MDL for Online Prediction
Minimum Description Length (MDL) is an important principle for induction and
prediction, with strong relations to optimal Bayesian learning. This paper
deals with learning non-i.i.d. processes by means of two-part MDL, where the
underlying model class is countable. We consider the online learning framework,
i.e. observations come in one by one, and the predictor is allowed to update
his state of mind after each time step. We identify two ways of predicting by
MDL for this setup, namely a static} and a dynamic one. (A third variant,
hybrid MDL, will turn out inferior.) We will prove that under the only
assumption that the data is generated by a distribution contained in the model
class, the MDL predictions converge to the true values almost surely. This is
accomplished by proving finite bounds on the quadratic, the Hellinger, and the
Kullback-Leibler loss of the MDL learner, which are however exponentially worse
than for Bayesian prediction. We demonstrate that these bounds are sharp, even
for model classes containing only Bernoulli distributions. We show how these
bounds imply regret bounds for arbitrary loss functions. Our results apply to a
wide range of setups, namely sequence prediction, pattern classification,
regression, and universal induction in the sense of Algorithmic Information
Theory among others.Comment: 34 page
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