Improving autocorrelation performance of Bernoulli sequence based on APAS theorem

Chaotic sequences have been widely used as pseudorandom sequences. But some well known chaotic sequence has poor autocorrelation performance, such as Bernoulli sequence, and their application are limited. Based on recently presented APAS theorem, we modified Bernoulli map to S-Bernoulli map, and S-Bernoulli sequence has excellent autocorrelation performance and simple structure, whereas its other performances are remained invariant or become better, and can be used more widely.