ABSTRACT
To further enhance code cardinality and coding flexibility, a third coding dimension can be added to 2-D optical codes, resulting in 3-D optical codes. This chapter discusses 3-D concatenated prime codes and multicarrier prime codes, in which the third coding dimension is supported by multiple spatial, fiber-optic, or wavelength-band channels. The 2-D carrier-hopping prime codes over GF(p) can be treated as wavelength-time matrices of pulses in distinct wavelengths and time slots. This property gives zero autocorrelation sidelobes and periodic cross-correlation functions of at most one. While the 3-D concatenated prime codes are basically 2-D wavelength-time codes, some wavelengths can be flexibly conveyed by a third coding channel, due to their special code structure. Targeted code cardinality and performance are easier to achieve in these 2-D prime codes than in their 1-D or 2-D counterparts, even with short code length.
