RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
Forthcoming seminars
Seminar calendar
List of seminars
Archive by years
Register a seminar

Search
RSS
Forthcoming seminars





You may need the following programs to see the files








Globus Seminar
June 29, 2018 15:30–16:15, Moscow, IUM (Bolshoi Vlas'evskii per., 11)
 


Trace reconstruction for the deletion channel

Yuval Peres

Microsoft Research
Video records:
MP4 646.1 Mb
MP4 1,254.4 Mb
MP4 311.5 Mb

Number of views:
This page:25
Video files:6

Yuval Peres


Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: In the trace reconstruction problem, an unknown string $x$ of $n$ bits is observed through the deletion channel, which deletes each bit with some constant probability q, yielding a contracted string. How many independent outputs (traces) of the deletion channel are needed to reconstruct $x$ with high probability?
The best lower bound known is linear in $n$. Until 2016, the best upper bound was exponential in the square root of $n$. In earlier work with F. Nazarov (STOC 2017), we improved the square root to a cube root using statistics of individual output bits and some inequalities for Littlewood polynomials on the unit circle. This bound is sharp for reconstruction algorithms that only use this statistical information. (Similar results were obtained independently and concurrently by De, O’Donnell and Servedio). Our main new result: If the string $x$ is random, then a subpolynomial number of traces suffices; the proof relies on comparison to a random walk.
(Joint works with Alex Zhai, FOCS 2017 and with Nina Holden & Robin Pemantle, COLT 2017.)

Language: English

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018