Instructor: Swastik Kopparty (firstname.lastname@example.org)
Class Time and Place: Thursdays, 12 noon – 3pm, in Hill 009
Office Hours: Wednesday 10:00-11:00 (Hill 432)
Prerequisites: basics of algorithms, complexity theory, probability, graph theory, linear algebra, mathematical maturity.
References: various online sources, scribe notes.
This course will be an introduction to the theoretical aspects of error-correcting codes, with many applications to complexity theory.
Students will take turns scribing the lectures, and the notes will be put up here. There will be 2-3 problem sets.
· Homework 1 (due Feb 4, but some parts are due earlier if you need permission to register)
· Homework 2 (due March 24)
· January 21: the main problems of coding theory, basic bounds on codes (notes)
· January 28: more bounds on codes, Shannon’s theorem for random errors (notes)
· February 4: codes based on polynomials (notes)
· February 11: concatenated codes (notes)
· February 18: BCH codes (notes)
· February 25: class cancelled (makeup class to be scheduled)
· March 3: expander codes, expander distance amplification (notes)
· March 10: class cancelled (makeup class to be scheduled)
· March 17: SPRING BREAK
· March 24: expander distance amplification, list-decoding (notes)
· March 31: list-decoding, list-decoding Reed-Solomon codes (notes)
· April 7: list-decoding concatenated codes, list-decoding Folded Reed-Solomon codes (notes)
· April 14: list-decoding Folded Reed-Solomon codes, locally decodable codes based on polynomials (notes)
· Tuesday April 19, 12 noon – 3pm: (NOTE UNUSUAL DAY) matching-vector codes (notes)
· April 21: multiplicity codes (notes)
· Tuesday April 26, 12 noon – 3pm: (NOTE UNUSUAL DAY) worst-case to average-case reductions, Fourier-based bounds for codes (notes)
· April 28: codes better than random (notes)