Extended carrier-hopping prime codes for wavelength-time optical code-division multiple access

A two-dimensional wavelength-hopping time-spreading coding scheme has been recently studied for optical code-division multiple access, owing to maturity in fiber-Bragg grating (FBG) and arrayed-waveguide grating (AWG) technologies. Most of the optical codes designed for the scheme were based on an assumption, which may not be true in high data-rate systems, that the number of chips is higher than the number of available wavelengths. To provide a flexible code design without the assumption, this paper studies and analyzes a new family of carrier-hopping prime codes with expanded cardinality and ideal correlation properties. Flexible implementation of programmable AWG- and FBG-based coding hardware by using the wavelength-shift property of the codes is discussed.