New Maximal-Period Sequences Using Extended Nonlinear Feedback Shift Registers Based on Chaotic Maps

Akio TSUNEDA  Yasunori KUGA  Takahiro INOUE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A   No.6   pp.1327-1332
Publication Date: 2002/06/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Papers Selected from 2001 International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC 2001))
maximal-period sequence,  NFSR,  chaotic map,  spreading sequence,  

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Nonlinear feedback shift registers (NFSRs), which can generate maximal-period sequences called de Bruijn sequences, are regarded as one-dimensional maps with finite bits by observing states of the registers at each time. Such one-dimensional maps are similar to the Bernoulli map which is a famous chaotic map. This implies that an NFSR is one of finite-word-length approximations to the Bernoulli map. Inversely, constructing such one-dimensional maps with finite bits based on other chaotic maps, we can design new types of NFSRs, called extended NFSRs, which can generate new maximal-period sequences. We design such extended NFSRs based on some well-known chaotic maps, which gives a new concept in sequence design. Some properties of maximal-period sequences generated by such NFSRs are investigated and discussed.