Design and performance analysis of wavelength/time (W/T) matrix codes for optical CDMA

Two-dimensional (2-D) codes for optical CDMA (OCDMA) are increasingly important because the code set size (cardinality) of such codes is large and the codes have good spectral efficiency, especially when compared to linear or direct sequence codes. As an example, the 2-D codes described in this paper (that use intensity modulation and direct detection, IM/DD) have a cardinality of 32, and their spectral efficiency is ∼0.5 bit/s/Hz when a guard-time is used to avoid intersymbol interference. The cardinality is readily increased to 64-80, using the techniques described in the paper. The next best 2-D codes of comparable cardinality that use IM/DD tend to have a lower spectral efficiency (going like 1/K, where K is the cardinality) because they do not support multiple entries per row or per column of the code matrix. To improve on the spectral efficiency of the codes described in this paper, bipolar codes must be considered. Two-dimensional codes or matrices can be generated from pseudoorthogonal (PSO) sequences by means of simple quasigraphical operations. Important results of this construction are that both the cardinality and the spectral efficiency or information spectral density of the set of matrices is higher than that of the generating set of sequences. The matrices can be interpreted (implemented) as space/time (S/T) or wavelength/time (W/T) matrix codes for OCDMA applications. The resultant matrix codes are robust, have high information spectral density, and are effective wavelength multipliers. This paper describes the design and construction of the matrices; analyzes their performance from a communications viewpoint; describes their use as codes for the asynchronous, concurrent communication of multiple users; and analyzes the bit error rate performance based on capturing and modeling a typical network topology and performing a numerical modeling of the system.