Constructing Optimal 2D Variable-Weight OOCs from Semicyclic Group Divisible Designs

Abstract

The OCDMA network using two Dimensional Variable-Weight Optical Orthogonal Codes (2D VWOOC) can support diverse Quality of Services (QoS) classes and multimedia services, and make the better use of bandwidth resources in fiber optical networks. To simplify practical implementation, the At Most One-Pulse Per Wavelength (AM-OPPW) restriction is often appended to a 2D VWOOC. In this paper, the upper bound on the size of AM-OPPW 2D VWOOCs is derived, semicyclic group divisible designs are introduced to construct AM-OPPW 2D VWOOCs, and an equivalence between optimal AM-OPPW 2D VWOOCs and Semicyclic Group Divisible Designs (SCGDDs) is established. Some direct and recursive constructions for SCGDDs are also presented. Consequently, several infinite families of optimal AM-OPPW 2D VWOOCs are obtained.