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

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.

Biography

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''.