Typical peak sidelobe level of binary sequences

Noga Alon, Simon Litsyn, Alexander Shpunt

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


For a binary sequence Sn = {si : i = 1, 2,...,n} ∈ {±1}n, n > 1, the peak sidelobe level (PSL) is defined as M(Sn) = maxk=1,2,n-1i=1n-k sisi+k|. It is shown that the distribution of M (Sn) is strongly concentrated, and asymptotically almost surely γ(Sn) = M(Sn)/√n In n ∈ [1 - o(1),√2]. Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known result due to Moon and Moser that the typical γ(Sn) ∈ [o(1/√In n), 2], and settles to the affirmative the conjecture of Dmitriev and Jedwab on the growth rate of the typical peak sidelobe. Finally, it is shown that modulo some natural conjecture, the typical γ(Sn) equals √2.

Original languageEnglish (US)
Article number5361502
Pages (from-to)545-554
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Aperiodic autocorrelation
  • Concentration
  • Peak sidelobe level (PSL)
  • Random binary sequences autocorrelation
  • Second moment method


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