Chaos Communication: An Overview of Exact, Optimum and Approximate Results Using Statistical Theory

Abstract

This paper overviews exact, optimum and approximate decoding and performance results for antipodal chaos shift-keying (CSK) in which a bit is transmitted by modulating a chaotic segment and decoded by use of the corresponding unmodulated reference segment. Both single-and multiple-user versions with both known-and transmitted-reference segments are considered, the so-called coherent and non-coherent cases. There are three main themes to the paper (i) the use of statistical likelihood theory for deriving optimum or improved decoders, (ii) the availability of mathematically exact theory for BER performance of decoders, (iii) qualitative statistical insights provided by simple Gaussian approximations to BER.