Classification of chaotic sequences with open-loop estimator - Optimal design for noisy environments

In this paper, an approach based on ergodic properties for classifying sequences is given. It is particularly robust due to the open loop structure of the detector. Unlike previous works in this direction, such as those concerning the inverse system approach, the detector is not uniquely determined by the transmitter (identical or subsystem thereof), but instead depends on the measurement noise model. The classification is optimized under such imperfect observation conditions. The method is introduced in general for the case of chaotic sequences generated by ergodic maps, and a special case is analyzed in detail to illustrate the method. This specila example resorts to Tchebychev maps and some additional symmetries to make a simple signaling scheme which is low in complexity on both transmitter and receiver sides, while at the same time relatively robust, due to the open-loop structure of the detector.