Design of binary sequences with tunable exponential autocorrelations and run statistics based on one-dimensional chaotic maps

This paper describes simple design methods of chaotic binary sequences with prescribed exponential autocorrelation properties and run statistics. We employ one-dimensional piecewise monotonic onto maps and a simple threshold function for generating such sequences. Some examples of such designs are also given. Furthermore, bounds on run statistics are discussed and compared to the result for sequences of general binary random variables.