Abstract
This study analyzes the autocovariance function of a binary sequence generated by switching between two stationary binary source sequences according to a third binary control sequence. Assuming that the three component sequences are mutually statistically independent, we derive a closed-form expression for the autocovariance function of the resulting sequence in terms of the mean values and autocovariance functions of the source and control sequences. The derived expression is decomposed into three contributions, which clarify the respective roles of the component statistics and lead to several representative special cases. As a concrete realization, chaos-based binary sequences generated by one-dimensional piecewise-linear maps are employed because their mean values and autocovariance functions can be controlled analytically. Numerical experiments are conducted for various combinations of positively correlated, sign-alternating, and zero-autocovariance component sequences. The numerical autocovariance functions show good agreement with the theoretical predictions in all examined cases, as supported by quantitative error assessments based on repeated simulations. The proposed analysis is not restricted to chaos-based sequences and is applicable to arbitrary stationary binary sequences satisfying the mutual-independence assumption.