Abstract
In this paper, we study a new class of two-dimensional codes, here called multilevel prime codes, with expanded code cardinality by relaxing the maximum cross-correlation function to any arbitrary positive integer. Besides having asymptotically optimal cardinality and zero autocorrelation sidelobes, these multilevel prime codes can be partitioned into a tree structure of multiple levels of subsets of code matrices. In each level, the number of subsets, the number of code matrices per subset, and the cross-correlation function of each subset are related to the level number. The performance of the new codes in an optical code-division multiple-access system with hard-limiting detection is analyzed. Our results show that the unique partition property of the multilevel prime codes supports a trade-off between code cardinality and performance for meeting different system requirements, such as user capacity and throughput.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
