## Abstract

A novel family of three-dimensional (3-D) wavelength/time/space codes for asynchronous optical code-division-multiple-access (CDMA) systems with “zero” off-peak autocorrelation and “unity” cross correlation is reported. Antipodal signaling and differential detection is employed in the system. A maximum of $[(W\times T+1)\times W]$ codes are generated for unity cross correlation, where *W* and *T* are the number of wavelengths and time chips used in the code and are prime. The conditions for violation of the cross-correlation constraint are discussed. The expressions for number of generated codes are determined for various code dimensions. It is found that the maximum number of codes are generated for $S\le \mathrm{min}(W,T)$, where *W* and *T* are prime and *S* is the number of space channels. The performance of these codes is compared to the earlier reported two-dimensional (2-D)/3-D codes for asynchronous systems. The codes have a code-set-size to code-size ratio greater than $W/S$. For instance, with a code size of 2065 ($59\times 7\times 5$), a total of 12,213 users can be supported, and 130 simultaneous users at a bit-error rate (BER) of ${10}^{-9}$. An arrayed-waveguide-grating-based reconfigurable encoder/decoder design for 2-D implementation for the 3-D codes is presented so that the need for multiple star couplers and fiber ribbons is eliminated. The hardware requirements of the coders used for various modulation/detection schemes are given. The effect of insertion loss in the coders is shown to be significantly reduced with loss compensation by using an amplifier after encoding. An optical CDMA system for four users is simulated and the results presented show the improvement in performance with the use of loss compensation.

© 2010 Optical Society of America

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