Two New Families of Synchronous Optical Codes for CDMA-Based Passive Optical Networks

In this paper, two new families of "synchronous" optical codes, called 1-D and 2-D synchronous multilevel prime codes (SMPCs), are constructed and analyzed for incoherent optical code-division multiple access (O-CDMA). With the benefit of synchronous transmission, the new algebraic codes have expanded cardinality and substantially increase the number of possible subscribers, thus potentially supporting rapid code switching and obscure-nature (privacy and military) communications. In addition, the SMPCs can be partitioned into a tree structure of multiple levels of subsets of codewords. Different cross-correlation functions are obtained from codewords coming from different subsets; code orthogonality is achieved among the codewords within each subset of the lowest level. As code performance is a strong function of the cross-correlation function, the performance of the codewords in use can be adjusted by choosing the subsets from which the codewords originate. The performances of the SMPCs are formulated and also verified by computer simulation. Our analysis shows that code performance can be optimized by applying an "in-order" subset-by-subset code-assignment method to simultaneous users. Besides supporting time-spreading and wavelength-time O-CDMA schemes, the new codes also find applications in passive optical networks and in spectral-amplitude-coding schemes.