On auto-correlation properties of random bit sequences by post-processing based on chaos theory

In Monte Carlo simulations, not only uncorrelated random sequences but also correlated ones are useful for simulating various kinds of stochastic phenomena. In this paper, we propose a simple post-processing method to generate aperiodic random bit sequences with prescribed (positive/negative) auto-correlations based on linear feedback shift registers (LFSRs) which realize the Bernoulli map with finite bits. By numerical experiments, we investigate some statistical properties of the random bit sequences generated by using the proposed post-processing.