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Statistical aspects of chaotic maps with negative dependence in a communications setting. (English) Zbl 0988.62072

Summary: It is shown that a class of tailed shift chaotic maps can be designed with substantial negative dependence, both linear and nonlinear, and that extended Perron-Frobenius theory gives their dependence structure. Using a simplified chaos-based communication system, it is shown that chaotic spreading sequences with low kurtosis and negative nonlinear mean-centred quadratic autocorrelations can improve bit-received accuracy. This quadratic form of nonlinear dependence is investigated and shown to be statistically sensible.

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62M99 Inference from stochastic processes
37H99 Random dynamical systems
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