Wavelength time optical orthogonal codes and phase encoding sequences for optical CDMA

UnrestrictedThere has been recent upsurge of interest in applying code division multiple access (CDMA) techniques to optical networks due to their enhanced data privacy, and simplicity of network control. There are two main approaches to code design for OCDMA systems. The first approach uses direct sequence encoding in which data sequence modulates the code sequence simply by switching it on or off. These codes, considered as 1-D optical orthogonal codes (OOC), employ {0,1} sequences with good correlation properties. In order to bring down the required chip rate within practical limits, 2-D {0,1} codes are used in which the code sequences consist of 2-D patterns with the second dimension corresponding to wavelength.; The second approach is via phase encoding in which the code sequences are collections of complex numbers of unit magnitude with each entry associated to a carrier of different wavelength. The phase of an element in the [lambda]th entry corresponds to the phase of the [lambda]th carrier. The focus of this thesis is on efficient code design for both approaches.; We begin by introducing some new bounds on the size of 1-D and 2-D OOCs. Subsequently, the focus is on explicit constructions for 2-D wavelength-time OOCs. We introduce four major constructions for wavelength-time OOCs, i.e., a method to map 1-D OOCs to 2-D OOCs, a method based on Reed-Solomon Codes, a method which concatenates a constant weight code with a Reed-Solomon based 2-D OOC and finally a function-plot method in which the values of an appropriately-chosen function are used to derive the 2-D codes. The functions used in the function plot construction include polynomial functions and rational functions.; Next, we consider phase-encoded OCDMA. We first derive a mathematical model for the output of this system and based on that introduce a metric to design codes for asynchronous transmission. Then, a connection between phase-encoding sequence design and PMEPR (peak to mean envelope power ratio) problem of OFDM systems is established. We construct a family of phase sequences based on generalized bent functions with desirable properties for asynchronous transmission