Constructions For Two-dimensional Optical Orthogonal Signature Pattern Codes

Optical orthogonal codes (OOCs) have been designed for OCDMA. A one dimensional (1-D) optical orthogonal code is a set of one-dimensional binary sequences having good auto and cross-correlations. OOC was first studied in1989. Since then there are many researches on OOCs and many results have been obtained.Most of the known results are on1-D OOCs. One limitation of1-D OOC is that the length of the sequence increases rapidly when the number of users or the weight of the code is increased, which means large bandwidth expansion is required if a big number of codewords is needed. To lessen this problem, two-dimensional OOC was invested. Recently some researchers are working on constructions and designs of2-D OOCs, but not too many results have been obtained.Two-dimensional optical orthogonal signature pattern code (OOSPC) is one kind of2-D OOCs. K. Kitayama found that OOSPCs are useful for transmitting digitized image pixels in optical code-division multiple-access (OCDMA) networks with multicore fiber in1994. However, it seems that researchers have not paid much attention to the constructions of OOSPCs as they have done for1-D OOCs and2-D OOCs.In this paper, we shall investigate direct and recursive constructions of OOSPCs. We give an equivalent relationship between OOSPCs and double cyclic packings. Based on this, we are able to use block design methods to obtain many new optimal OOSPCs with weight three or four. For direct constructions, we use backtracking algorithm to search OOSPCs with small code length. We also use the idea of exchanging base blocks to improve the efficiency of the backtracking algorithm.