The Existence Of Optimal 2-D Optical Orthogonal Codes

In recent years, code-division multiple access (CDMA) system has been widely used in satellite communication, mobile communication, etc. Each of the users in a CDMA system is assigned a unique binary code which is used to distinguish the user's signal from that of oth-ers'. Since the usable bandwidth sets limits to the satellite and mobile communication system, CDMA technique can't express its feature greatly. However, the problem have been solved with optical code-division multiple access (OCDMA) and CDMA combined efficiently.Because of great advantage in safety protection and anti-interference, OCDMA system help us communicate in different areas conveniently. In the OCDMA system, there are good auto-correlation and cross-correlation between these binary codes. These binary codes are called the optical orthogonal codes (OOC). From its application point of view, higher chip rate is needed with the number of one-dimensional OCDMA users (or the weight of codes) increas-ing, and thus it require broader band expansion. So the number of one-dimensional OCDMA can easily contradict with system performance.In 1992, Park E. proposed two-dimensional OCDMA system model on the basis of time multiplex and spare multiplex. Subsequently, Yang G.C. etc. proposed the theoretical model of wavelength optical orthogonal code in 1997. In OCDMA system, by spreading 2-D codes in both wavelength and time, the chip rate can be reduced considerably and the bandwidth utilization can be improved effectively. These make the performance of OCDMA got further ascent. In recent years, people make a lot of research on the constructions of two-dimensional optical orthogonal code (2-D OOC) which focusing on how to improve the cardinality of the codes and the performance of system, etc.This paper mainly discuss the constructions of 2-D OOC, when k=3 andλ=1. It is di-vided into four parts. In the first part, we mainly introduce the background of 2-D OOC and its definition. Then we list the known results and our paper's main conclusions. In the second part, we establish the corresponding relationship of 2-D OOC with strictly cyclic packing design by revealing the combinational characteristics of 2-D OOC. Then we give the definitions of some auxiliary designs. In the third part, we presents the existence of 2-D OOC for small orders. In the fourth part, the main conclusions are given by using the recursive constructions.