Abstract-In this paper, two construction schemes of variable-weight optical orthogonal codes (OOCs) for asynchronous optical-code-division multiple-access (O-CDMA) systems are proposed. The first scheme uses pairwise balanced design (PBD), which is a research topic in combinatorial theory. PBD produces a family of blocks with unequal block size. Therefore, PBD can be used to construct OOCs with variable code weight. The lower bound of the code size of the codes from PBD is formulated in this paper. A second scheme employes packing design with a partition to generate blocks with unequal block sizes. The variable-weight OOCs can be constructed by partitioning a larger weight codeword into a family of codes with a smaller code weight. The upper bound and lower bound of the code size of the second scheme are discussed. The bit-error-rate (BER) performances of the two proposed codes are evaluated analytically in this paper. The simulation results show that the codes from the first scheme have the same BER performance as that of conventional code, while the second scheme has a larger maximum number of simultaneous users than that of conventional codes.Index Terms-Bit-error rate (BER), optical-code-division multiple access (O-CDMA), optical orthogonal codes (OOCs), packing design, pairwise balanced design (PBD), variable weight.

A new family of two-dimensional (2-D) wavelength/ time optical orthogonal codes (OOCs) for asynchronous optical code division multiple access (OCDMA) systems is proposed. The construction scheme uses the difference family (DF), which is an assemblage of difference sets in the combinatorial theory. It is proven that the proposed codewords satisfy the correlation properties required for the asynchronous OCDMA systems. The code dimension of the proposed codes is more flexible than that of the conventional 2-D codewords. The performance of the system with the proposed codes is analyzed by using the Markov-chain method. Numerical results show that the bit error rate (BER) has a minimal value given the number of simultaneous users. It is also observed that the maximum number of simultaneous users of the system can be achieved by properly choosing both the code weight and cross correlation of the 2-D OOCs.

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