Quickest Sequence Phase Detection

TL;DR

This paper investigates the fundamental limits and constructions of phase detection sequences capable of identifying subsequences from noisy observations, including multiple sequences and various noise models.

Contribution

It derives bounds on minimal subsequence length for phase detection, introduces sequence constructions, and analyzes the trade-offs and limits in multiple sequence scenarios under different noise models.

Findings

Bounds on minimal k for phase detection sequences

Sequence constructions for reliable detection

Strict separation between phase detection and channel coding limits

Abstract

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.