Quickest Sequence Phase Detection

Lele Wang, Sihuang Hu, Ofer Shayevitz

Research output: Contribution to journalArticlepeer-review


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 , 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.

Original languageEnglish
Article number7930515
Pages (from-to)5834-5849
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - Sep 2017
Externally publishedYes


  • De Bruijn sequence
  • Lovász local lemma
  • adversarial noise
  • linear feed-back shift register
  • multiple access channel
  • positioning system
  • probabilistic noise
  • zero-error capacity


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