Due to the fact that we lack a general construction method of multiple-length (ML) optical orthogonal codes (OOCs), a general construction method with high efficiency for ML OOCs with arbitrary cross-correlation is presented. The main idea of the method is to construct a variable-length mapping sequence with unparallel positions, with which to map short-length OOCs into long-length OOCs to realize the general construction of ML OOCs with correlation value with high efficiency by the Johnson bound. The cardinality of multiple-length mapping sequences is derived. Based on the cardinality, the fundamentals of constructing the aforementioned multiple-length mapping sequences are presented and proved. The construction method of ML OOCs with arbitrary cross-correlation is given. Simulation results show that the method can construct ML OOCs with arbitrary ; the applications of ML OOCs show that the method is practical for constructing ML OOCs to support multiple service.
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