Gianluca Setti

Chaotic complex spreading sequences for asynchronous DS-CDMA. I. System modeling and results

This paper and its companion are devoted to the evaluation of the impact of chaos-based techniques on communications systems with asynchronous code division multiple access. Sequences obtained by repeating a truncated and quantized chaotic time series are compared with classical m-sequences and Gold sequences by means of a performance index taken from communication theory which is here defined and thoroughly discussed. This analysis reveals that, unlike conventional sequences, chaotic spreading codes can be generated for any number of users and allocated bandwidth. Numerical simulations are reported, showing that systems based on chaotic spreading sequences perform generally better than the conventional ones. Some analytical tools easing the comprehension of these advantages are summarized.

Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications

The application of chaotic dynamics to signal processing tasks stems from the realization that its complex behavior becomes tractable when observed from a statistical perspective. Here we illustrate the validity of this statement by considering two noteworthy problems-namely, the synthesis of high-electromagnetic compatibility clock signals and the generation of spreading sequences for direct-sequence code-division communication systems, and by showing how the statistical approach to discrete-time chaotic systems can be applied to find their optimal solution. To this aim, we first review the basic mathematical tools both intuitively and formally; we consider the Perron-Frobenius operator its spectral decomposition and its tie to the correlation properties of chaotic sequences. Then, by leveraging on the modeling/approximation of chaotic systems through Markov chains, we introduce a matrix/tensor-based framework where statistical indicators such as high-order correlations can be quantified. We underline how, for many particular cases, the proposed analysis tools can be reversed into synthesis methodologies and we use them to tackle the two above mentioned problems. In both cases, experimental evidence shows that the availability of statistical tools enables the design of chaos-based systems which favorably compare with analogous nonchaos-based counterparts.

Chaotic complex spreading sequences for asynchronous DS-CDMA. Part II. Some theoretical performance bounds

For pt.I see G. Mazzini et al., vol.44, pp.937-47 (Oct. 1997). This paper and its companion (Part I) are devoted to the evaluation of the impact of chaos-based techniques on communications systems with asynchronous Code Division Multiple Access. In Part I, a performance index was introduced and exploited to a priori estimate the performance of DS-CDMA communications systems based on chaotic spreading sequences, and to compare it to that of conventional systems. Here, tools from nonlinear dynamical system theory are employed to give a formal ground for those results. Analytical bounds on the expected partial cross correlation between spreading sequences obtained by quantizing and repeating a chaotic time series are derived, ensuring general applicability of such a technique in a real environment. Further analytical arguments guarantee that, when particular chaotic generators are used, expected performance is not worse than that of a well-behaving communications system. This analysis ensures also that, unlike conventional sequences, chaotic spreading codes can be generated for any number of users and allocated bandwidth.

An approach to information propagation in 1-D cellular neural networks. II. Global propagation

For pt.I see P. Thiran et al., ibid., vol.45, no.8, pp.777-89 (1998). This second of two papers studies how and when a global propagation of information, introduced as initial condition, is possible through a one-dimensional (1-D) Cellular Neural Network (CNN) with connections between nearest neighbors only. We will focus on circular arrays, which have the most regular structure, we will show that periodic solutions exist, and we will compute one of them analytically. We will also study their stability.

An approach to information propagation in 1-D cellular neural networks-Part I: Local diffusion

Keywords: neurone ; Non-Linear Modelling ; Neural Network Reference LANOS-ARTICLE-1998-004View record in Web of Science Record created on 2004-12-03, modified on 2017-05-12

Spectral properties of chaos-based FM signals: theory and simulation results

This paper addresses the problem of generating constant-envelope wideband (CEW) signals, for which applications are emerging both in telecommunications (as information carriers) and in digital/power electronics (to aid the synthesis of timing signals which favor electromagnetic compliance). A flexible generation technique consists in driving a frequency modulation (FM) modulator with random or chaotic sequences. Mathematical tools for predicting some spectral properties of random-FM and chaotic-FM CEW signals are herein introduced by commenting on recent results and presenting novel ones in a coherent framework.

Implementation and Testing of High-Speed CMOS True Random Number Generators Based on Chaotic Systems

We present the design and the validation by means of suitably improved randomness tests of two different implementations of high-performance true-random number generators which use a discrete-time chaotic circuit as their entropy source. The proposed system has been developed from a standard pipeline Analog-to-Digital converter (ADC) design, modified to operate as a set of piecewise-linear chaotic maps. The evolution of each map is observed and quantized to obtain a random bit stream. With this approach it is possible to obtain, on current CMOS technology, a data rate in the order of tens of megabit per second. Furthermore, we can also prove that the design is tamper resistant in the sense that a power analysis cannot leak information regarding the generated bits. This makes the proposed circuit perfectly suitable for embedding in cryptographic systems like smarts cards, even more so if one consider that it could be easily obtained by reconfiguring an existing pipeline ADC. The two prototypes have been designed in a 0.35-μm and 0.18-μm CMOS technology, and have a throughput of, respectively, 40 Mbit/s and 100 Mbit/s. A comparison between measured results and other high-end commercial solutions shows a comparable quality with a operating speed that is one order of magnitude faster.

Chaos-based asynchronous DS-CDMA systems and enhanced Rake receivers: measuring the improvements

Results of recent theoretical investigations highlighted that the use of chaos in direct-sequence code-division multiple access (DS-CDMA) systems may lead to nonnegligible improvements in communication quality for several scenarios. We here briefly review the main steps in this derivation and report the experimental verifications of the corresponding theoretical prediction. With this, we confirm that chaos-based spreading sequences outperform classical pseudo-random sequences in at least two important cases. Over nonselective channels, the ability of chaos-based spreading of minimizing multiple-access interference leads to a measured 60% improvement in P/sub err/ with respect to classical spreading. Over selective channels, the possibility of jointly optimizing chaos-based spreading and Rake receiver profiles leads to improvements of up to 38% in P/sub err/ with respect to systems with either conventional spreading or conventional Rake policies.

Rakeness in the Design of Analog-to-Information Conversion of Sparse and Localized Signals

Design of random modulation preintegration systems based on the restricted-isometry 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 trade-off 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 rakeness-based design leads to nonnegligible improvements in both cases.

Low-Complexity Multiclass Encryption by Compressed Sensing

The idea that compressed sensing may be used to encrypt information from unauthorized receivers has already been envisioned but never explored in depth since its security may seem compromised by the linearity of its encoding process. In this paper, we apply this simple encoding to define a general private-key encryption scheme in which a transmitter distributes the same encoded measurements to receivers of different classes, which are provided partially corrupted encoding matrices and are thus allowed to decode the acquired signal at provably different levels of recovery quality. The security properties of this scheme are thoroughly analyzed: first, the properties of our multiclass encryption are theoretically investigated by deriving performance bounds on the recovery quality attained by lower-class receivers with respect to high-class ones. Then, we perform a statistical analysis of the measurements to show that, although not perfectly secure, compressed sensing grants some level of security that comes at almost-zero cost and thus may benefit resource-limited applications. In addition to this, we report some exemplary applications of multiclass encryption by compressed sensing of speech signals, electrocardiographic tracks and images, in which quality degradation is quantified as the impossibility of some feature extraction algorithms to obtain sensitive information from suitably degraded signal recoveries.