Two-dimensional spatial signature patterns

Abstract

An optical orthogonal signature pattern code (OOSPC) is a collection of (0,1) two-dimensional (2-D) patterns with good correlation properties (i.e., high autocorrelation peaks with low sidelobes, and low cross-correlation functions). Such codes find applications, for example, to parallelly transmit and access images in "multicore-fiber" code-division multiple-access (CDMA) networks. Up to now all work on OOSPCs has been based on an assumption that at most one pulse per column or one pulse per row and column is allowed in each two-dimensional pattern. However, this restriction may not be required in such multiple-access networks if timing information can be extracted from other means, rather than from the autocorrelation function. A new class of OOSPCs is constructed without the restriction. The relationships between two-dimensional binary discrete auto- and cross-correlation arrays and their corresponding "sets" for OOSPCs are first developed. In addition, new bounds on the size of this special class of OOSPCs are derived. Afterwards, four algebraic techniques for constructing these new codes are investigated. Among these constructions, some of them achieve the upper bounds with equality and are thus optimal. Finally, the codes generated from some constructions satisfy the restriction of at most one pulse per row or column and hence can be used in applications requiring, for example, frequency-hopping patterns.