Quickest Sequence Phase Detection.

A phase detection sequence is a length- $n$ cyclic sequence, such that the location of any length- $k$ contiguous subsequence can be determined from a noisy observation of that subsequence. In this paper, we derive bounds on the minimal possible $k$ in the limit of $n\to \infty $ , and describe some sequence constructions. We further consider multiple phase detection sequences, where the location of any length- $k$ contiguous subsequence of each sequence can be determined simultaneously from a noisy mixture of those subsequences. We study the optimal trade-offs between the lengths of the sequences, and describe some sequence constructions. We compare these phase detection problems to their natural channel coding counterparts, and show a strict separation between the fundamental limits in the multiple sequence case. Both adversarial and probabilistic noise models are addressed. [ABSTRACT FROM AUTHOR]