An information signal transmission method by chaotic systems (Q2754831)

[See also the review Zbl 0977.94504.]NEWLINENEWLINENEWLINEThe authors discuss a method of binary signal transmission by means of two ``noise-scale close'' maps \(f_0\) and \(f_1\), each of which generates a chaotic dynamical system. A transmitter converts each element \(v_j\in \{0,1\}\), \(j\geq 0,\) of the signal \(v_0v_1v_2\cdots \) into a trajectory of the map \(f_{v_j}\) proceeding the packet \(\{x_{jm+s}\}_{s=0,1,\dots,m-1}\), where \(x_{jm+s+1}=f_{v_j}(x_{jm+s})\) and the integer \(m\) depends on \(f_0\), \(f_1\) and ``noise''. Getting a packet \(\{\overline x_{jm+s}=x_{jm+s}+ \text{noise}\}_{s=0,1,\dots,m-1}\), the receiver has to decide whether this sequence corresponds to \(v_j=0\) or \(v_j=1\), or, equivalently, which of the trajectories of the maps \(f_0\), \(f_1\) is hidden in the packet obtained. NEWLINENEWLINENEWLINEThe authors describe an algorithm for recovering trajectories based on the anti-synchronization properties of the maps: for an interval \(J\) of length \(2\varepsilon \), where \(\varepsilon \) is the magnitude of the noise, the lengths of preimages \(f_i^{-s}J\), \(i=0,1\), \(s=0,1,\dots,\) decrease as \(s\) increases. The identification algorithm works if the sets \(f_0^{-m}J\) and \(f_1^{-m}J\) are distant from each other by not less then \(2\varepsilon \).