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Seminar: Syndrome decoding of Reed-Muller codes and tensor decomposition over finite fields

Abstract: 

In this talk, we will look at decoding Reed-Muller codes beyond their minimum distance when the errors are random (i.e., in the binary symmetric channel). A recent beautiful result of Saptharishi, Shpilka and Volk showed that for binary Reed-Muller codes of length n and degree n - O(1), one can correct polylog(n) random errors in poly(n) time (which is well beyond the worst-case error tolerance of O(1)). We will see two efficient algorithms as well as a different proof of the same result, where the decoding is done given the polylog(n)-bit long syndrome vector of the corrupted codeword:
1) The first is via. a connection to the well-studied `tensor decomposition problem'.
2) The second via. a reduction to finding all common roots of a space of low degree polynomials, which is also of independent interest.

Joint work with Swastik Kopparty

Speaker: 
Aditya Potukuchi
Location: 
CoRE A 301
Event Date: 
11/15/2017 - 11:00am
Committee: 
Rutgers/DIMACS Theory of Computing
Event Type: 
Seminar
Organization: 
Rutgers University