This course covers the concept of proximity gaps for Reed-Solomon codes. By the end of the course, learners will understand the main theorem statement regarding correlated agreement and proximity gaps, as well as how to apply the Berlekamp-Welch decoder in different sets. The course teaches common notations related to Reed-Solomon codes, error terms, generalizations to different sets, decoders, and applications of prior work. The teaching method includes theoretical explanations and practical examples. This course is intended for individuals interested in advanced coding theory and error-correction techniques.
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
