This paper first reviews an extended family of carrier-hopping prime codes (CHPCs) with expanded (asymptotically optimal) cardinality and ideal correlation properties. They are designed for wavelength-time optical code-division multiple-access (O-CDMA) applications with broadband lasers, in which there are extra number of available wavelengths. The performance of the extended CHPCs is analyzed and compared to a wavelength-grouping scheme using the original CHPCs. Furthermore, the traditional pessimistic chip-synchronous assumption used in performance analysis of 2-D codes with cross-correlation functions of at most one is removed for a more realistic error probability. In addition to the Gaussian approximation, we introduce in this paper a more accurate combinatorial method, expecially when the number of simultaneous users is small.
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