Explicit Evaluations of Correlation Functions of Chebyshev Binary and Bit Sequences Based on Perron–Frobenius Operator

Tohru KOHDA  Akio TSUNEDA 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E77-A  No.11  pp.1794-1800
Publication Date: 1994/11/20
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
Category: Chaos and Related Topics
Keyword: 
chaos,  correlation function,  nonlinear ergodic map,  Chebyshev binary and bit sequence,  Perron–Frobenius operator, 

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Summary: 
Binary sequences with good correlation properties are required for a variety of engineering applications. We previously proposed simple methods to generate binary sequences based on chaotic nonlinear maps. In this paper, statistical properties of chaotic binary sequences generated by Chebyshev maps are discussed. We explicitly evaluate the correlation functions by means of the ensemble–average technique based on the Perron–Frobenius (P–F) operator. As a consequence, we can confirm an important role of the P–F operator in evaluating statistics of chaos by means of the ensemble-average technique.