Levenshtein improved the aperiodic Welch bound by using the key idea that the weighted mean square aperiodic correlation of any sequence subsets over the complex roots of unity is equal to or greater than that of the set comprised of all sequences over the complex roots of unity. Following this key idea, I will introduce Generalized Levenshtein Bound (GLB) [1] for quasi-complementary sequence sets (QCSS), which refer to a set of two-dimensional arrays with low aperiodic correlation sums. The GLB, in the form of a fractional quadratic function of the simplex weight vector, is non-convex in general and thus its tightening is challenging. In the second part of this talk, I will present a frequency-domain optimization approach which tightens GLB in an analytical way [2].

This talk will be based on my following papers:

[1] Z. Liu, Y. L. Guan and W. H. Mow, “A Tighter Correlation Lower Bound for Quasi-Complementary Sequence Sets,” IEEE Transactions on Information Theory, vol. 60, no. 1, pp. 388-396, Jan. 2014.

[2] Z. Liu, Y. L. Guan and W. H. Mow, “Asymptotically Locally Optimal Weight Vector Design for a Tighter Correlation Lower Bound of Quasi-Complementary Sequence Sets,” IEEE Transactions on Signal Processing, vol. 65, no. 12, pp. 3107-3119, June 2017.