Abstract
The existence of binary sequences with specific aperiodic autocorrelation and cross correlation properties is investigated. Relationships are determined among the size of a sequence set, the length of the sequences n, the maximum autocorrelation sidelobe magnitude \alpha , and the maximum cross correlation magnitude \beta . The principal result is the proof of the existence of sequence sets characterized by certain combinations of n, \alpha , and \beta . The proof makes use of a new lower bound to the expected size of sequence sets constructed according to an explicit random procedure. For large n , the sequence set size is controlled primarily by the cross correlation constraint \beta . Two consequences of the existence theorem are 1) a demonstration that large sequence sets exist for which the maximum autocorrelation sidelobe and cross correlation magnitudes vanish almost as fast as the inverse square root of the sequence length (l/\sqrt{n}); 2) a new proof of the Gilbert bound of coding theory.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.