A new class of carrier-hopping codes for code-division multiple-access optical and wireless systems

Carrier-hopping codes, a collection of two-dimensional (2-D) patterns with good correlation properties, find applications in frequency-hopping code-division multiple-access (CDMA) wireless and wavelength-hopping CDMA fiber-optic systems. This kind of codes were usually designed under the assumptions that one pulse per row is used in the 2-D patterns and the number of available carriers is the same as code weight. While the assumptions restrict code cardinality, there are scenarios in which the number of available carriers is more than the actual number of carriers needed in the patterns. To provide flexible code design without these assumptions, this letter reports a new family of carrier-hopping codes with expanded cardinality, while maintaining ideal correlation properties. The cardinality of the new codes is shown to be asymptotically optimal.