Explore the intricacies of Reed-Solomon Codes and their proximity gaps in this 21-minute IEEE conference talk. Delve into common notations, motivating problems, and the main theorem statement on correlated agreement. Examine error terms and generalizations to different sets. Learn about prior work, applications, and various decoders, including the Berlekamp-Welch decoder. Gain insights from experts Eli Ben-Sasson, Dan Carmon, Yuval Ishai, Swastik Kopparty, and Shubhangi Saraf as they discuss the application of Berlekamp-Welch to w(2) and its implications for Reed-Solomon Codes.
Overview
Syllabus
Intro
Common notations (Reed-Solomon codes)
Motivating problem
Main theorem statement — correlated agreement
proximity gaps
The error term
Generalizations to different sets
Prior Work and Applications Prior work
Decoders
What do we decode?
The Berlekamp Welch decoder
The Berlekamp-Welch decoder in F,(2)
Applying Berlekamp Welch to w(2)
Applying Berlekamp-Welch to w(2)
Taught by
IEEE FOCS: Foundations of Computer Science
