We propose feedback-limited NFSRs (nonlinear feedback shift registers) which can generate periodic sequences of period 2k-1, where k is the length of the register. We investigate some characteristics of such periodic sequences. It is also shown that the scale of such NFSRs can be reduced by the feedback limitation. Some simulation and experimental results are shown including comparison with LFSRs (linear feedback shift registers) for conventional M-sequences and Gold sequences.

We define discretized Markov transformations and find an algorithm to give the number of maximal-period sequences based on discretized Markov transformations. In this report, we focus on the discretized dyadic transformations and the discretized golden mean transformations. Then we find an algorithm to give the number of maximal-period sequences based on these discretized transformations. Moreover, we define a number-theoretic function related to the numbers of maximal-period sequences based on these discretized transformations. We also introduce the entropy of the maximal-period sequences based on these discretized transformations.

This paper deals with the method for generation of maximal-period sequences which are designed by properly quantizing the variable state of a class of one-dimensional piecewise-linear onto maps. We confirmed that the proposed method enables us to generate many maximal-period sequences from such maps including De-Bruijn cases.

This paper presents design of spreading codes for asynchronous DS-CDMA systems. We generate maximal-period sequences with negative auto-correlations based on one-dimensional maps with finite bits whose shapes are similar to piecewise linear chaotic maps. We propose an efficient search algorithm to find such maximal-period sequences. This algorithm makes it possible to find many kinds of maximal-period sequences with sufficiently long period for practical CDMA applications. We also report that maximal-period sequences can outperform conventional Gold sequences in terms of bit error rate (BER) in asynchronous DS-CDMA systems.

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.