Statistical Properties of Real-Valued Sequences Generated by Chebyshev maps Hiroshi Fujisaki

Abstract: Recently binary or real-valued sequences generated by Chebyshev maps are proposed as spreading sequences in $\mathrm{D}\mathrm{S}/\mathrm{C}\mathrm{D}\mathrm{M}\mathrm{A} $ systems. In this note, we consider sequences of real-valued functions of bounded variation, which include binary functions, of iterates generated by Chebyshev maps, and evaluate the rate of mixing of such sequences using the Perron-Frobenius operator associated with the Chebyshev maps. 1Introduction During the past decade, binary or real-valued sequences generated by one-dimensional ergodic maps have been proposed for spreading sequences and its statistical properties in $\mathrm{D}\mathrm{S}/\mathrm{C}\mathrm{D}\mathrm{M}\mathrm{A} $ system have been studied. In such ergodic maps, especially Chebyshev maps have been intensively studied in the following. Binary pseud0-random sequences generated by Chebyshev maps, or briefly referred to as Chebyshev binary sequences, are firstly proposed in [1], and asufficient condition is derived for akind of ergordic maps to generate sequences of i.i.d. (independent and identicaly distributed) binary random variables in [2]. Based on the evaluations of correlation functions of so called Chebyshev binary sequence