Gianluca Setti
IEEE Circuits and Systems joint Chapter of the Vancouver/Victoria Sections
Centre for Scientific Computing Seminar (in conjunction with PIMS/MITACS)

Professor Gianluca Setti
DI, University of Ferrara
Ferrara, Italy
University of Bologna
Bologna, Italy


(Presentation is available in pdf format.)

Tuesday, March 28, 2006, 2:30 pm
IRMACS, ASB 10900 - Presentation Studio
Simon Fraser University


Recent developments have highlighted that a statistical approach may greatly benefit the study of discrete-time chaotic system (maps). In this case, in fact, critical dependence on initial condition, probably the widest known feature of chaotic behavior, prevents the study of single trajectories from giving information which are globally valid. On the contrary, a highly regular behaviour exists for the distribution of the points describing the evolution of a set of trajectories at each iteration step. We will formalize this approach by introducing a theoretical framework that is based on the classical Perron-Frobenius Operator (PFO), which accounts for the evolution of the probability densities describing the distribution of the system state variable at each iteration step. We then focus on Piecewise Affine Markov (PWAM) maps, and by specializing the set of theoretical tools that we have introduced, we will show how such maps can be considered as stochastic processes generators with tunable statistical features. Such a well-developed theoretical framework can be applied to several topics related to IT, such as

  • 1 - Spreading sequence design for Direct Sequences Code Division Multiple Access (DS-CDMA)
  • 2 - EMI (Electro-Magnetic Interference) reduction
  • 3- True random number generation

    Among them, we will focus on the optimization of DS-CDMA system in an asynchronous environment. The first aim is to ground the theoretical characterization of the performance achievable in a asynchronous DS-CDMA system when chaos-based spreading sequences are substituted for classical Gold or m-sequences. A first advantage of this method for sequence generation is that all the limitations on sequence number and/or length which are intrinsic in discrete-math shift-register based approaches. Additionally and more important, it can be also proved that chaos-based spreading is able to achieve the absolute minimum multiple-access interference (MAI). Hence, when multiple-access interference is the main cause of errors in the communication, chaos-based spreading allows to obtain the optimum system which can be computed to have an average 15.47% increase in capacity with respect to systems adopting random or pseudo-random spreading. Non-average performance can be optimized to obtain peak of more than 60% increase in capacity. Theoretical predictions have been also confirmed by a prototype system including 8 transmitters and a receiver matched with one of the transmitters. Chaos-based spreading has also been tested against other typical problems in the design of DS-CDMA systems and has been proved to enhance the system performance in terms of lost-bits in the sequence acquisition phase at link startup as well as in terms of reduced bit-error probability in certain multipath propagation scenarios. We will then tackle the problem of performance evaluation using the concept of Shannon capacity taken from information theory. More specifically we assume the existence of a coding/decoding pair that is able to transmit information through this channel with a vanishing error probability and evaluate the capacity of the system with the maximum rate at which such an errorless link may operate. As a noteworthy result, it can be shown that the same chaos-based spreading that minimizes multiple-access interference is actually able to reach the absolute maximum Shannon capacity in the classical two-user case, as well as when the number of users and the spreading factor grow to infinity. This result is of great practical importance since it proves that the adoption of chaos-based spreading will certainly maximize performance in an asynchronous DS-CDMA system for any possible receiver. Finally we will evaluate the impact of adopting chaos-based spreading in the case of multi-code DS-CDMA systems (where more than one spreading sequence is assigned to each of the users, so that MAI has both a synchronous and an asynchronous component) as well as for Sensors Networks based on Ultra-Wide Band communication.


    Gianluca Setti received a Dr. Eng. degree (with honors) in Electronic Engineering and a Ph.D. degree in Electronic Engineering and Computer Science from the University of Bologna, Bologna in 1992 and in 1997, respectively, for his contribution to the study of neural networks and chaotic systems. From May 1994 to July 1995 he was with the Laboratory of Nonlinear Systems (LANOS) of the Swiss Federal Institute of Technology in Lausanne (EPFL) as visiting researcher. Since 1997 he has been with the School of Engineering at the University of Ferrara, Italy, where he is currently an Associate Professor of Circuit Theory and Analog Electronics. His research interests include nonlinear circuits, recurrent neural networks, implementation and application of chaotic circuits and systems, statistical signal processing, electromagnetic compatibility, wireless communications and sensor networks.

    Dr. Setti received the 1998 Caianiello prize for the best Italian Ph.D. thesis on Neural Networks and he is co-recipient of the 2004 IEEE CAS Society Darlington Award.

    He served as an Associate Editor for the IEEE Transactions on Circuits and Systems - Part I (1999-2002, area: Nonlinear Circuits and Systems, 2002-2004, area: Chaos and Bifurcations), and for the IEEE Transactions on Circuits and Systems - Part II (2004-2006). Currently he is acting as Deputy-Editor-in-Chief, for the IEEE Circuits and Systems Magazine (since 2004) and as Editor-in-Chief for the IEEE Transactions on Circuits and Systems - Part II (since January 2006).

    He was the 2004 Chair of the Technical Committee on Nonlinear Circuits and Systems of the of the IEEE CAS Society, a Distinguished Lecturer (2004-2005) and a member of the Board of Governors (since 2005) of the same society. Dr. Setti was also the Technical Program Co-Chair of NDES2000 (Catania) the Track Chair for Nonlinear Circuits and Systems at ISCAS2004 (Vancouver), and the Special Sessions Co-Chair at ISCAS2005 (Kobe) and ISCAS2006 (Kos).

    He is co-editor of the book Chaotic Electronics in Telecommunications (CRC Press, Boca Raton) and one of the guest editors of the May 2002 special issue of the IEEE Proceedings on ``Applications of Non-linear Dynamics to Electronic and Information Engineering''.

  • Last updated Monday March 27 15:31:26 PST 2006.