Optical Orthogonal Codes with Unequal Auto- and Cross- Correlation Constraints

Abstract

An optical orthogonal code (OOC)is collection of binary sequences with good auto-and cross-correlation properties; they were defined by Salehi and others as a means of obtaining code division multiple access on optical networks. Up to now all work on OOC's have assumed that the constraint placed on the auto- correlation and that placed on the cross-correlation are the same. In this paper we consider codes for which the two constraints are not equal. Specifically, we develop bounds on the size of such OOC's and demonstrate construction techniques for building them. The results demonstrate that a significant increase in the code size is possible by letting the auto- correlation constraint exceed the cross-correlation constraint. These results suggest that for a given performance requirement the optimal OOC may be one with unequal constraints.<P>This paper also views OOC's with unequal auto- and cross-correlation constraints as constant-weight unequal error protection (UEP) codes with two levels of protection. The bounds derived are interpreted from this viewpoint and are compared with previous work on UEP codes.