Quickest sequence phase detection

Lele Wang, Sihuang Hu, Ofer Shayevitz

Abstract: We consider the problem of designing a length-n binary sequence, such that the location of any length-k contiguous subsequence can be determined from a noisy observation of that subsequence. We derive bounds on the minimal possible k in the limit of n → ∞, and describe some sequence constructions. Both adversarial and probabilistic noise models are addressed. Two applications of the problem include fast positioning and card tricks.