## 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.

© 2009 Optical Society of America

Full Article | PDF Article**OSA Recommended Articles**

^{n}extended-prime codes

Jian-Guo Zhang, Wing C. Kwong, and Stelly Mann

Appl. Opt. **36**(26) 6664-6667 (1997)

Yue-Kai Huang, Ivan Glesk, Christoph M. Greiner, Dmitri Iazikov, Thomas W. Mossberg, Ting Wang, and Paul R. Prucnal

Opt. Express **15**(12) 7327-7334 (2007)

^{n}Prime Code

Jian-Guo Zhang, Lian-Kuan Chen, Kwok-Wai Cheung, Wing C. Kwong, and A.B. Sharma

Appl. Opt. **38**(34) 7151-7152 (1999)