Information sources using chaotic dynamics

A sequence of binary random variables has found significant applications in modem digital communication systems. For such sequences, several kinds of linear feedback shift register sequences have been proposed. It is, however, well known in probability theory that the Bernoulli shift is a fundamental theoretic model of a sequence of independent identically distributed (i.i.d.) binary random variables. In this paper after reviewing fundamental subjects of chaotic dynamics, in particular a close relationship between information sources and Markov chains, we give the generation method of sequences of i.i.d. binary random variables using chaotic dynamics. Such a generation method is given as a sufficient condition composed of simple symmetric properties for some class of ergodic maps. Furthermore, we give the applications of such sequences: (1) to running-key sequences for stream cipher systems and (2) to a color image communication system through code-division multiple access channels and its extended version, a digital watermarking system. In addition, the performance of spread spectrum codes generated by a Markov chain is theoretically evaluated in asynchronous direct-sequence/code-division multiple access systems.