Adaptive 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 consider the problem of designing phase detection sequences that allow adaptive phase detection for different noise levels at the detector. We discuss two detection scenarios: depending on the noise level, the detector adaptively chooses the length k of the observation period, or adaptively chooses the detection resolution. We establish the optimal rate regions in both settings.