Quadratic-Congruence Carrier-Hopping Prime Code for Multicode-Keying Optical CDMA

In this paper, we study a new family of carrier-hopping prime codes (CHPCs), so-called quadratic- congruence CHPC (QC-CHPC), with expanded code cardinality by relaxing the maximum cross-correlation function to two (i.e., lambda
_c
= 2). An application of the new code is for multicode keying in wavelength-time optical code-division multiple access (O-CDMA), in which each user is assigned M = 2
^m
code matrices to represent m data bits per symbol. The advantages are that 1) a lower baud multicode-keying O-CDMA system can support a higher bit rate and 2) user's code obscurity is enhanced, as compared to the transmission of one code matrix (per user) for each data bit one in conventional "on-off keying" O-CDMA systems. Our performance analysis shows that there is a trade-off between the code performance and hardware complexity/speed related to the choice of M, for a given bit rate.