Extended multilevel prime codes for optical CDMA

In this paper, a new family of "multilevel" wavelength-time codes with expanded code cardinality, flexible code length, zero autocorrelation sidelobes, and the maximum cross-correlation function of any arbitrary positive integer n is constructed and analyzed. Besides having asymptotically optimal cardinality, the new codes can be partitioned into n levels, such that the cross-correlation function between any two code matrices in level l is at most l, where 1 ¿ l ¿ n. The hardlimiting performance of these multilevel codes is analyzed algebraically. Our results show that the unique partitioning property of these multilevel codes supports a trade-off between code cardinality and performance for meeting different system requirements, such as user capacity and throughput.