Instructor: Mary Wootters
TA: Reyna Hulett
When and where? T/Th 10:30-11:50am, Sapp Center for Science Teaching and Learning (STLC), Room 119.
Course Description: Introduction to the theory of error correcting codes, emphasizing algebraic constructions and diverse applications throughout computer science and engineering. Topics include basic bounds on error correcting codes; Reed-Solomon and Reed-Muller codes; list-decoding, list-recovery and locality. Applications may include communication, storage, complexity theory, pseudorandomness, cryptography, streaming algorithms, group testing, and compressed sensing.
Prerequisites: Linear algebra, basic probability (at the level of, say, CS109, CME106 or EE178) and "mathematical maturity" (students will be asked to write proofs). Familiarity with finite fields will be helpful but not required.
What do I need to do? Three homework assignments and a final project.
The following is a tentative schedule. It is subject to change, especially the lectures that have not happened yet.
| Tuesday | Thursday |
|---|---|
| 1/9. Lecture 1: Logistics and the basics of coding theory.
Homework 0 "released". |
1/11. Lecture 2: Intro to finite fields and linear codes; Hamming and GV bounds.
Optional reading: Forney's introduction to finite fields. Homework 1 released. |
| 1/16. Lecture 3: More linear codes. Application: McEliece Cryptosystem; Asymptotics, Hamming and GV bounds.
Homework 0 due. |
1/18. Lecture 4: Singleton and Plotkin bounds; Reed-Solomon Codes!!! |
| 1/23. Lecture 5: More Reed-Solomon Codes! Welch-Berlekamp and Berlekamp-Massey algorithms | 1/25. Lecture 6: Binary codes! BCH codes, code concatenation. HW1 due; HW2 released. |
| 1/30. Lecture 7: More Concatenated Codes and the Zyablov bound | 2/1. Lecture 8: Algorithmic applications of RS codes: streaming, compressed sensing, group testing |
| 2/6. Lecture 9: Random errors and efficiently achieving capacity on the BSC | 2/8. Lecture 10: List-Decoding! (List-decoding capacity theorem and the Johnson bound)
Relevant reading: Extensions to the Johnson Bound (Guruswami and Sudan 2001) HW2 due; HW3 released. |
| 2/13. Lecture 11: Guruswami-Sudan Algorithm | 2/15. Lecture 12: List recovery and applications |
| 2/20. Lecture 13: List recovery and applications II | 2/22. Lecture 14: Folded Reed-Solomon Codes HW3 due; start thinking about your projects! |
| 2/27. Lecture 15: Reed-Muller Codes | 3/1. Lecture 16: Locality. Project proposals due. |
| 3/6. Lecture 17: Local list-decoding and applications (Goldreich-Levin, Kushilevitz-Mansour) | 3/8. Lecture 18: Applications in storage: Regenerating codes from RS codes |
| 3/13. Lecture 19: Guest lecture: Marco Mondelli | 3/15. Lecture 20: Guest lecture: Marco Mondelli |
| 3/20. -- | 3/22. Final projects due (by email to marykw) |
Please follow the instructions on the homework sets for doing and submitting your homework, and note the grading policies below.
Homework:
Project: