CORRELATION BOUNDS ON SOME NONLINEAR SEQUENCE SETS

Abstract

Pseudo-Noise (PN) sequences with low out-of-phase autocorrelation and low cross- correlation values have many applications as synchronization codes, masking or scrambling codes, and for white noise signals in communication systems, signal sets in Code Division Multiple Access (CDMA) communications, key stream generators in stream cipher cryptosystems, random number generators, and as testing vectors in hardware design. Besides, sequences with large linear span increase the linear complexity of the sequence, thus makes difficult to generate a replica of the sequences for eavesdropping and jamming purposes. This dissertation work focuses on study of various nonlinear sequences and their correlation properties. Bounds on correlation functions of signals play a major part in evaluating the theoretical performance of the spreading sequences and in sequence set selection for reliable, efficient and secure communication. Welch and Sidelnikov bounds have long been used as a benchmark for testing the merit of signal sets in the design of good CDMA sequence families. Besides, partial correlations are equally important in practice. This dissertation work is focused on determination of the peak partial correlation bounds of binary signals over fading channels. Binary signals with 2-level autocorrelation values such as maximal length sequences, GMW sequences, Cascaded GMW sequences, quadratic residue sequences, Hall sextic sequences, have importance in synchronization, radar, cryptography etc. In this dissertation, determination of upper bound on peak partial autocorrelation of cascaded GMW sequences using underlying interleaving structure of m-sequence is considered. Synchronous CDMA systems require large set of families with low cross- correlation values as signature sequences. Bent and Semi-bent signal sets have the best nonlinearity possible which makes them more secure to use. This dissertation focuses on obtaining lower bound on maximum correlation of binary signals over fading channels.