Statistical aspects of chaotic maps with negative dependence in a communications setting

TLDR: It is shown that a class of tailed shift chaotic maps can be designed with substantial negative dependence, both linear and non‐linear, and that extended Perron–Frobenius theory gives their dependence structure.

Abstract: Summary. It is shown that a class of tailed shift chaotic maps can be designed with substantial negative dependence, both linear and non-linear, 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 non-linear mean-centred quadratic autocorrelations can improve bit-received accuracy. This quadratic form of non-linear dependence is investigated and shown to be statistically sensible.