Séminaire INFRES TELECOM ParisTech / en Amphi Rubis
Organisateurs:Hugues Randriam &Dario Rossi
Orateur:Simon Litsyn (EE-Systems,Tel Aviv University)
Titre: A la recherche du temps et de la position perdus
Résumé: For a binary (plus/minus one) finite sequence,the peak sidelobe level (PSL) is defined as the maximum,over nonzero shifts,of the scalar product of the sequence with its aperiodically shifted version. Binary sequences with low PSL are of importance for synchronization in TIME and determining POSITION and distance to an object. In theoretical physics,study of the PSL landscape was introduced by Bernasconi via the so-called Bernasconi model,which is fascinating for the fact of being completely deterministic,but nevertheless having highly disordered ground states (sequences with the lowest PSL) and thus possessing striking similarities to the real glasses (spin glass models),with many features of a glass transition exhibited.
The problem of designing and characterizing sequences with low PSL has been attacked for at least fifty years,however our knowledge is still far from being satisfactory.
In the talk I will survey the main open issues and report on several new results:
- We show that the typical PSL of binary sequences is proportional to \sqrt{n ln n},thus improving on the best earlier known result due to Moon and Moser and settling to the affirmative a conjecture of Dmitriev and Jedwab;
- We show that the maximum of PSL in m-sequences is proportional to 2^{m/2} ln m,thus disproving a long-standing conjecture of it being 2^{m/2}.
The results are partly due to cooperation with N. Alon,Ye. Domoshnitsky,A. Shpunt and A. Yudin.
