Chaos Communication: A Case of Statistical Engineering

Abstract

The paper gives a statistically focused selective view of chaos-based communication which uses segments of noise-like chaotic waves as carriers of messages, replacing the traditional sinusoidal radio waves. The presentation concerns joint statistical and dynamical modelling of the binary communication system known as “chaos shift-keying”, representative of the area, and leverages the statistical properties of chaos. Practically, such systems apply to both wireless and optical laser communication channels. Theoretically, the chaotic waves are generated iteratively by chaotic maps, and practically, by electronic circuits or lasers. Both single-user and multiple-user systems are covered. The focus is on likelihood-based decoding of messages, essentially estimation of binary-valued parameters and efficiency of the system is in terms of the probability of bit decoding error. The emphasis is on exact theoretical results for bit error rate, their structured approximations and engineering interpretations. Design issues, optimality of performance, interference and fading are other topics considered. The statistical aspects of chaotic synchronization are involved in the modelling of optical systems. Empirical illustrations from an experimental laser-based system are presented. The overall aim is to show the use of statistical methodology in unifying and advancing the area.