Aperiodic autocorrelation properties of sequences and arrays.

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The study of the aperiodic autocorrelation properties of binary sequences began in the 1950s and continues to be of central importance in diverse digital transmission systems, including radar information processing, power control for multicarrier wireless transmission, and optical time domain reflectometry. Sequences and arrays whose aperiodic autocorrelations are collectively small in relation to the sequence or array size correspond to signals whose transmission wastes very little energy and which can be recovered efficiently at the receiver.Traditionally, the analysis of autocorrelation properties has concentrated on the periodic case, where the presence of rich mathematical structure admits many theoretical techniques. But the aperiodic case is much more significant in practice, because it arises naturally in so many application contexts. Although conventional wisdom has long been that aperiodic autocorrelations display little structure, and that often the only realistic means of analysis is computer search, there have been several recent indications to the contrary.The short-term objectives of the program are to study particular classical problems in this area for which recent results have opened up new research directions. The long-term objective is to identify emerging methods, and develop new ones, for studying aperiodic autocorrelations of large sequences and arrays. This is becoming increasingly important as modern digital communications systems are less likely to be restricted to the use of smaller sequences and arrays. The general scientific approach will be to combine tools and insights from discrete mathematics, computing science, and digital communications engineering. Where appropriate, experimental computation will be used to reveal patterns, identify key examples, improve intuition, and so point the way to new theoretical results.