Generation of chaos-based random bit sequences with prescribed auto-correlations by post-processing using linear feedback shift registers

Post-processing scheme using linear feedback shift registers (LFSRs) for generat-ing chaos-based random bit sequences with infinite period for use in Monte-Carlo methods isdiscussed. We theoretically analyze auto-correlation functions of choatic binary sequences gen-erated by the Bernoulli chaotic map and a class of binary funcitons. The theoretical analysescan be applied to the LFSR-based post-processing for generating random bit sequences withprescribed auto-correlations because LFSRs can be regarded as a finite bit approximation ofthe Bernoulli map. Some results of numerical experiments are also given.