Yuval Peres: Trace reconstruction for the deletion channel

Speaker: Yuval Peres, Microsoft Research, Redmond

Date: Tuesday, May 02, 2017

Time: 4:00 PM to 5:00 PM

Refreshments: 3:45 PM

Public: Yes

Location: Kiva G449

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Host: Ankur Moitra

Contact: Deborah Goodwin, 617.324.7303, dlehto@csail.mit.edu

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Reminders to: seminars@csail.mit.edu, theory-seminars@csail.mit.edu

Reminder Subject: TALK: Yuval Peres: Trace reconstruction for the deletion channel

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 (due to Holenstein, Mitzenmacher, Panigrahy and Wieder 2008) was exponential in the square root of $n$. We improve the square root to a cube root using statistics of individual output bits and some complex analysis; this bound is sharp for reconstruction algorithms that only use this statistical information. (Joint work with Fedor Nazarov, STOC 2017; similar results were obtained independently and concurrently by De, OÂ’Donnell and Servedio). In very recent work with Alex Zhai, we showed that If the string $x$ is random and $q<1/2$, then a subpolynomial number of traces suffices.

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Created by Deborah Goodwin Email at Thursday, April 27, 2017 at 9:02 AM.