Constructing chaotic discrete sequences for digital communications based on correlation analysis

We introduce a model of chaotic systems that can provide a predictable probability distribution to generate discrete sequences for digital communications. Some well-known chaotic maps belong to its special cases. We generalize the spirit of a paper by Kohda and Tsuneda (1997) to explicitly express the covariance functions of the chaotic discrete sequences generated by this model. Based on the model, a scheme is proposed to construct the chaotic orthonormal discrete sequences, which are characterized by the asymptotic normalized (partial) δ-like autocovariance and near-zero cross covariance. Compared with the conventional algebraic sequences, such chaotic discrete sequences have quite a large number of choices. All empirical results well correspond to theoretic prediction