Extended multilevel prime codes for optical-CDMA networks with algebraic code switching

A class of algebraic codes for incoherent optical code-division multiple access, so-called extended multilevel prime codes, was recently studied. They have asymptotic optimal cardinality and possess a unique tree structure of multiple levels of subsets of codewords; codewords in different subsets have different cross-correlation values for adjustable code performance. In this paper, the performance of the codes under an optimized method of assigning codewords to simultaneous users is formulated. In addition, how the tree structure, large cardinality, and the codes' algebraic properties potentially support rapid codeword switching and physical-layer network security are investigated.