[Nrg-l] FW: Sem in Prob: Statistical Aspects of Chaos
Mark Crovella
crovella at cs.bu.edu
Tue Dec 5 21:22:21 EST 2006
Looks pretty interesting!
Mark
-----Original Message-----
From: owner-prob-sem at math.bu.edu on behalf of Murad Taqqu
Sent: Tue 12/5/2006 6:12 PM
To: prob-sem at math.bu.edu
Subject: Sem in Prob: Statistical Aspects of Chaos
SERIES: Prob. and Stat. Seminar at Boston University
SPEAKER: Tony Lawrance (University of Warwick, Coventry, UK)
TITLE: Statistical Aspects of Chaos and Chaos Communication
DATE: Tuesday, December 12, 2006
TIME: 10 am - noon
PLACE: MCS 135
(Boston University, 111 Cummington Street, Mathematics Department)
ABSTRACT:
This presentation will be introductions to both statistical
aspects of chaos and chaos-based communication performance
modelling. The first is more generic and presents the main
aspects of chaos of interest to statisticians. By chaos here we just
mean continuous-valued time series which are generated by simple
nonlinear mathematical recursions, such as tent, modulo, logistic and
Chebyshev maps. If you do not know the generating process, but just
consider numerical realizations, they look "stochastic" and have
well-defined statistical properties. There is an analogy with random
number generators, and more practically with laser generated series.
Interestingly, one can think of a chaotic sequence as the most extreme
opposite of an independent sequence. The statistical properties of
interest are marginal distribution and dependence, both linear and
nonlinear, and a sum of squares quantity, and not the sensitivity and
dimensionality of traditional chaos theory.
The second part introduces the area of chaos-based communications, a
topic originating in radio- and laser- based communications research.
Instead of the traditional sinusoidal radio waves, chaotic ones are
used. Although still in the experimental stage, there are perceived
qualities of security and in capacity from being "spread-spectrum",
and also some serious practical questions of
implementation and performance. This talk will outline one particular
mathematical model for chaos communication, the binary "chaos shift
keying" system, and study its performance in terms of bit error,
that is when a 1 is decoded at the receiver as a 0 and vice-versa.
Decoders are essentially statistical estimators which can be invented
or derived by statistical principles, and it is their properties which
are important. The speaker's work has involved developing exact
theory of bit error performance, replacing inaccurate
"engineering" approximations and giving more insight. One
particular theoretical concern has been to identify a system with
minimum bit error. It has been shown how this can be achieved by
minimising a chaotic sum of squares and that it requires use of a
particular chaotic map. There are a variety of other possible topics,
such as alternative measures of performance, likelihood optimal
decoders, jamming and multi-user systems. Four references to the
speaker's work on this topic are:
EMAIL: A.J.Lawrance at warwick.ac.uk
REFERENCES:
1. Statistical aspects of chaotic maps with negative dependency in a
communications setting, with N Balakrishna.
J. R. Statistic. Soc. B (2001), 63, 843-853.
2. Exact calculation of bit error rates in communication systems with
chaotic modulation, with G Ohama. IEEE Transactions on Circuits and
Systems -I: Fundamental Theory and Applications, (2003), 50,
1391-1400.
3. Bit error probability and bit outage rate in chaos communication,
with G.Ohama. Circuits, Systems and Signal Processing, (2005), 24,
5, 519-534.
4. Performance analysis and optimization of multi-user differential
chaos-shift-keying communication systems, with J Yao. IEEE
Transactions on Circuits and Systems -I: Regular Papers (2006),
53, 9, 2075-2091.
Announcements will be done by email and through the Web Page:
http://math.bu.edu/people/murad/
--
__________________________________________________
| Murad S. Taqqu | Dept. of Mathematics |
| murad at math.bu.edu | 111 Cummington Street |
| TEL: (617) 353-3022 | Boston University |
| FAX: (617) 353-8100 | Boston, MA 02215-2411 |
| |
| http://math.bu.edu/people/murad |
|__________________________________________________|
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