Parrondo's paradox involves two losing games of chance. The paradox is that a winning situation is produced when the two games are played in a random sequence in accordance with fixed probabilities. In this paper we investigate the relationship between these parameters and the entropy rates of the games.

We de ne a general procedure for simulating a given discrete distribution using a sequence of i.i.d. random variables. This procedure is used to prove that a natural information-theoretic bound on the number of samples required to simulate the distribution can be arbitrarily approached in a limiting sense. c © 1999 Elsevier Science B.V. All rights reserved

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of entropies of (standard) full shifts. When a shift space with overlaps arises as a model for a discrete dynamical system with a finite set of overlapping neighborho...

We introduce novel information-entropic variables—a Point Divergence Gain (Ω α ), a Point Divergence Gain Entropy (Iα), and a Point Divergence Gain Entropy Density (Pα)—which are derived from the Rényi entropy and describe spatio-temporal changes between two consecutive discrete multidimensional distributions. The behavior of Ω α is simulated for typical distributions and, together with Iα and ...

The measure-theoretic definition of Kullback-Leibler relative-entropy (KL-entropy) plays a basic role in the definitions of classical information measures. Entropy, mutual information and conditional forms of entropy can be expressed in terms of KL-entropy and hence properties of their measure-theoretic analogs will follow from those of measure-theoretic KL-entropy. These measure-theoretic defi...

A system is presented for transform coding of imagery. Specifically, the system uses the 2-D discrete cosine transform (DCT) in conjunction with adaptive classification, entropy-constrained trelliscoded quantization, optimal rate allocation, and adaptive arithmetic encoding. Adaptive classification, side rate reduction, and rate allocation strategies are discussed. Entropy-constrained codebooks...

This paper is dedicated to entropy coding for scalable video compression based on three-dimensional discrete wavelet transform (3-D DWT). A new simple bit-plane entropy coding of wavelet subband matrices is proposed. Practical results show that 3-D DWT video codec with proposed entropy coding allows to increase the encoding speed 2-3 times for the same quality level in comparison with x.264 cod...

We consider weak solutions of (hyperbolic or hyperbolic-elliptic) systems of conservation laws in one-space dimension and their approximation by finite difference schemes in conservative form. The systems under consideration are endowed with an entropy-entropy flux pair. We introduce a general approach to construct second and third order accurate, fully discrete (in both space and time) entropy...

Abstract This document expands upon the relationship between discrete and continuous entropy given in (Phys. Rev. Lett. 11

We are concerned with the approximation of undercompressive, regularizationsensitive, nonclassical solutions of hyperbolic systems of conservation laws by high-order accurate, conservative, and semidiscrete finite difference schemes. Nonclassical shock waves can be generated by diffusive and dispersive terms kept in balance. Particular attention is given here to a class of systems of conservati...