A study on random bit sequences with prescribed auto-correlations by post-processing using linear feedback shift registers

There are several attempts to use chaotic nonlinear maps for random number generation. Theoretically, some chaotic maps can produce balanced and i.i.d. (independent and identically distributed) binary sequences. Also, chaotic binary sequences with prescribed auto-correlations can be generated. However, it is difficult to generate aperiodic sequences with prescribed auto-correlation properties by analog circuits or digital circuits only. In this paper, we propose a simple post-processing by linear feedback shift registers for generating random bit sequences with prescribed (positive/negative) auto-correlations. We perform some numerical experiments for investigating the effects of the proposed post-processing.