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arXiv · 1605.09038

Quickest Sequence Phase Detection

Lele Wang·Sihuang Hu·Ofer Shayevitz
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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.

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Lele Wang, Sihuang Hu, Ofer Shayevitz. 2016-05-29. Quickest Sequence Phase Detection. https://doi.org/10.1109/tit.2017.2705159

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