Two-dimensional optical orthogonal codes for fiber-optic CDMA networks

Several constructions of two-dimensional (2-D) codes have been proposed to overcome the drawbacks of nonlinear effects in large spread sequences of one-dimensional (1-D) unipolar codes in fiber-optic code-division multiple-access (FO-CDMA) networks. Wavelength-time (W/T) encoding of the 2-D codes is practical in FO-CDMA networks. W/T codes reported so far can be classified mainly into two types: 1) hybrid codes, where one type of sequence is crossed with another to improve the cardinality and correlation properties and 2) conversion of 1-D sequences to 2-D codes to reduce the "timelike" property. This paper describes the basic principles of a new family of wavelength/time multiple-pulses-per-row (W/T MPR) codes, for incoherent FO-CDMA networks, which have good cardinality, spectral efficiency, and minimal cross correlation values. In addition, an expression for the upper bound on the cardinality of W/T MPR codes is derived. Another feature of the W/T MPR codes is that the aspect ratio can be varied by a tradeoff between wavelength and temporal lengths. The correlation properties of W/T MPR codes are verified by simulation using Matlab. For given wavelength x time dimensions, various W/T codes, whose cardinalities are known, are compared, and it is shown that the W/T MPR family of codes have better cardinality and spectral efficiency than the other W/T codes. Performance analysis of the W/T MPR codes and their limiting cases is carried out for various parameter variations such as the dimensions of wavelength, time, and weight of the code.