Improved constructions and bounds for 2-D optical orthogonal codes

Some bounds and efficient constructions for 2-D optical orthogonal codes (OOC) in which spreading is carried out over both wavelength and time are provided. Such codes are of current practical interest as they enable fiber-optic communication at lower chip rates. The bounds provided include 2-D versions of the Johnson bound as well as a novel bound based on an extension of the Johnson bound to non-binary alphabets. The Singleton bound is recovered as a special instance of this bound. Several constructions of 2-D OOC are presented in the paper and almost all of these are either optimal or else asymptotically optimum in the sense of having code size that equals or approaches the maximum possible as the size of the code matrix (along the dimension associated to time) approaches infinity. Our principal construction views each wavelength-time OOC as the plot of a function and the functions employed in the constructions belonging to this class are either polynomials or rational functions. Other constructions include a technique for deriving 2-D OOCs from 1-D OOCs using the Chinese remainder theorem, a means of making use of MDS codes to construct 2-D OOCs satisfying the one-pulse-per-wavelength constraint and a method of concatenating a constant-weight code with a one-pulse-per-wavelength 2-D OOC to generate OOCs with at most one pulse per wavelength