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11
2008b). Invariant measures of tunable chaotic sources: robustness analysis and efficient estimation
 IEEE Transactions on Circuits and Systems  I. Accepted, available online
"... In this paper a theoretical approach for studying the robustness of the chaotic statistics of piecewise affine maps with respect to parameter perturbations is discussed. The approach is oriented toward the study of the effects that the nonidealities derived from the circuit implementation of these ..."
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In this paper a theoretical approach for studying the robustness of the chaotic statistics of piecewise affine maps with respect to parameter perturbations is discussed. The approach is oriented toward the study of the effects that the nonidealities derived from the circuit implementation of these chaotic systems have on their dynamics. The ergodic behavior of these systems is discussed in detail adopting the approach developed by Boyarsky and Góra, with particular reference to the family of Sawtooth maps, and the robustness of their invariant measures is studied. Although the paper is particularly focused on this specific family of maps, the proposed approach can be generalized to other piecewise affine maps considered in the literature for ICT applications. Moreover, in the paper an efficient method for estimating the unique invariant density for stochastically stable piecewise affine maps is proposed. The method is an alternative to MonteCarlo methods and to other methods based on the discretization of the FrobeniusPerron operator. 1
Compressive sensing of localized signals: Application to analogtoinformation conversion,” ISCAS
, 2010
"... Abstract—Compressed sensing hinges on the sparsity of signals to allow their reconstruction starting from a limited number of measures. When reconstruction is possible, the SNR of the reconstructed signal depends on the energy collected in the acquisition. Hence, if the sparse signal to be acquired ..."
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Cited by 4 (1 self)
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Abstract—Compressed sensing hinges on the sparsity of signals to allow their reconstruction starting from a limited number of measures. When reconstruction is possible, the SNR of the reconstructed signal depends on the energy collected in the acquisition. Hence, if the sparse signal to be acquired is known to concentrate its energy along a known subspace, an additional “rakeness ” criterion arises for the design and optimization of the measurement basis. Formal and qualitative discussion of such a criterion is reported within the framework of a wellknown AnalogtoInformation conversion architecture and for signals localized in the frequency domain. Nonnegligible inprovements are shown by simulation. I.
Rakeness in the design of AnalogtoInformation conversion of sparse and localized signals
 IEEE Transactions on Circuits and Systems I: Regular Papers
, 2012
"... tems based on the restrictedisometry property may be suboptimal when the energy of the signals to be acquired is not evenly distributed, i.e. when they are both sparse and localized. To counter this, we introduce an additional design criterion, that we call rakeness, accounting for the amount of e ..."
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Cited by 3 (1 self)
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tems based on the restrictedisometry property may be suboptimal when the energy of the signals to be acquired is not evenly distributed, i.e. when they are both sparse and localized. To counter this, we introduce an additional design criterion, that we call rakeness, accounting for the amount of energy that the measurements capture from the signal to be acquired. Hence, for localized signals a proper system tuning increases the rakeness as well as the average SNR of the samples used in its reconstruction. Yet, maximizing average SNR may go against the need of capturing all the components that are potentially nonzero in a sparse signal, i.e., against the restricted isometry requirement ensuring reconstructability. What we propose is to administer the tradeoff between rakeness and restricted isometry in a statistical way by laying down an optimization problem. The solution of such an optimization problem is the statistic of the process generating the random waveforms onto which the signal is projected to obtain the measurements. The formal definition of such a problems is given as well as its solution for signals that are either localized in frequency or in more generic domain. Sample applications, to ECG signals and small images of printed letters and numbers, show that rakenessbased design leads to nonnegligible improvements in both cases. I.
Digitized Chaos for PseudoRandom Number Generation in Cryptography
"... Random numbers play a keyrole in cryptography, since they are used, e.g., to define enciphering keys or passwords [1]. Nowadays, the generation of random numbers is obtained referring to two types of devices, that are often properly ..."
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Random numbers play a keyrole in cryptography, since they are used, e.g., to define enciphering keys or passwords [1]. Nowadays, the generation of random numbers is obtained referring to two types of devices, that are often properly
pseudorandom number generators Quantifiers for randomness of chaotic Rapid response Subject collections
, 2009
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On The Shannon Capacity Of ChaosBased Asynchronous CDMA Systems
"... We here compare the limit performance asynchronous DSCDMA systems based on different set of spreading sequences, namely chaosbased, ideal random, Gold codes and maximumlength codes. To do so we consider the Shannon capacity associated to each of those systems that is itself a random variable depe ..."
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We here compare the limit performance asynchronous DSCDMA systems based on different set of spreading sequences, namely chaosbased, ideal random, Gold codes and maximumlength codes. To do so we consider the Shannon capacity associated to each of those systems that is itself a random variable depending on the relative delays and phases between different users. The statistical features of such a random capacity are evaluated by means of the MonteCarlo simulation of a proper adjustment of the classical formula for vector AWGN channels. It is shown that chaosbased spreading results in a nonnegligible increase of the capacity.
Estimation of the Entropy and Other Dynamical Invariants for Piecewise Affine Chaotic Maps
"... In this paper we discuss an efficient iterative method for the estimation of the chief dynamical invariants of chaotic systems based on stochastically stable piecewise affine maps (e.g., the invariant measure, the Lyapunov exponent as well as the KolmogorovSinai entropy). Referring to the theory ..."
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In this paper we discuss an efficient iterative method for the estimation of the chief dynamical invariants of chaotic systems based on stochastically stable piecewise affine maps (e.g., the invariant measure, the Lyapunov exponent as well as the KolmogorovSinai entropy). Referring to the theory developed by C. Liverani, we provide a theoretical tool for determining a priori a sufficient number of iterations that guarantees a given estimation accuracy. The proposed method represents an alternative to the MonteCarlo methods and to other methods based on the discretization of the FrobeniusPerron operator, such as the well known Ulam’s method. Our estimation method converges not slower than exponentially and it requires a computation complexity that grows linearly with the iterations. The proposed approach can be used to efficiently estimate any order statistics of a symbolic source based on a piecewise affine mixing map. 1
A Model for Computational Collapse of 1D Chaotic Maps
"... AbstractThis paper reports a method to dissect the orbit structure of quantized chaotic maps of the unit interval. The ¯nite precision of computer arithmetic yields a spatially discrete dynamical system whose behavior is quite di®erent from that expected on the continuum of real numbers. All com ..."
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AbstractThis paper reports a method to dissect the orbit structure of quantized chaotic maps of the unit interval. The ¯nite precision of computer arithmetic yields a spatially discrete dynamical system whose behavior is quite di®erent from that expected on the continuum of real numbers. All computed orbits are eventually periodic; which is in stark contrast to the theoretical dynamics on the real line. The dynamical behavior of quantized 1D maps of the unit interval is characterized in terms of a) The period and quantity of the cycles where every orbit eventually lands after a ¯nite number of iterations of the map; and b) The length and quantity of the paths that lead to these orbits. An e±cient algorithm to compute these descriptors is proposed. The simulation results are theoretically justi¯ed in particular cases.