Two-dimensional optical CDMA systems based on MWOOC with generalized MPS codes

Two-dimensional (2-D) codes for optical code-division multiple access (O-CDMA) systems can increase the number of subscribers and simultaneous users rather than one-dimensional time-spreading codes. The multiple-wavelength optical orthogonal code (MWOOC), which is one of the 2-D codes proposed by Kwong et al. in 2005, uses two kinds of codes. One is an optical orthogonal code (OOC) as a time-spreading code, and the other is a modified prime sequence (MPS) code as a wavelength-hopping code. The MWOOCs have some advantages compared with other 2-D codes especially in high bit-rate OCDMA systems. The only drawback of the MWOOC is that the code weight is no greater than the smallest prime of the number of wavelengths when the number of wavelengths is not prime. Since the code weight is equal to the peak value of the auto-correlation function, it degrades bit error rate (BER) performance of the system. Moreover, a nonprime integer makes the total code cardinality small, and thus the maximum number of subscribers in a nonprime case is much smaller than that in a prime case. Meanwhile, a generalized class of MPS codes, which includes the class of original MPS codes as its subclass, was presented recently by the authors. The important property of the generalized MPS codes is that the codes can be constructed over not only prime fields but also extension fields, i.e. GF(p^m) where p is a prime number and m is a positive integer. It has been shown that the correlation property of the generalized MPS codes is the same as that of the original MPS codes. The use of the generalized MPS codes solve the problem of the MWOOC. That is, nonprime numbers can be also taken as the number of wavelengths without degrading BER performance or reducing code cardinality. This paper investigates properties and BER performance of the MWOOCs employing the generalized MPS codes.