General Info:
- Lecturer:
Madhu
Sudan; MD 339; email: first name at cs dot
harvard dot edu; Office Hours: MW 4:30-5:30pm
- Teaching
Fellow: Chi-Ning Chou: MD 138, email:
chiningchou at g.harvard.edu; Office hours: TuFr 4:30pm-5:30pm (MD 1st floor
common space).
- Lecture Time and Location: MW 3pm-4:15pm
in Northwest
B108.
Other links for the course:
- Course announcement: Brief
description of the course.
- Grading policy.
- Piazza
site: All announcements will be routed through this
site - so please sign up right away!!
- Canvas
site: You will need access to Canvas to submit your
problem sets.
Problem Sets:
- There were 6 psets in the course + 1 (diagnostic) pset
0. Email madhu if you would like access to them for
teaching your course.
Announcements:
- Make sure you've signed up for piazza and know how to
access your canvas account. If any of these is a problem,
reach out to Madhu or Chi-Ning.
- Please sign up for scribing! Signup instructions and
sheet here.
Template for scribing here (preamble,
sample.tex).
Topics, Calendar and
Handouts:
- Lecture 01 (Mon. 01/27): Introduction. Hamming's Paper.
Codes, Distance, Examples, Limits and Algorithms. Notes
from 2008 (use these notes for technical content;
not for grading policy etc.!). Reading [Chapter
1 and Chapter
2 from the text.].
Scribe notes (tex, pdf).
- Lecture 02 (Wed. 01/29): Shannon's Theorems. Noiseless
coding. Noisy Coding. Shannon Capacity. Notes
from 2008. Reading [Chapter
6]. Scribe notes (tex,
pdf).
- Lecture 03 (Mon. 02/03):
Converse to Shannon's theorem. Random codes. Linear codes.
Gilbert-Varshamov theorems. Asymptotics of
error-correcting codes. Notes
from 2008. Reading [Chapter
1 and Chapter
4]. Scribe notes (tex,
pdf).
- Lecture 04 (Wed. 02/05): Simple Impossibility Results
for Codes. (Pigeonhole argument, packing argument,
geometric arguments). Reading [Chapter
4 and Chapter
8]. Notes
from 2008, Scribe notes (tex,
pdf).
- Lecture 05 (Mon. 02/10): Bounds on codes continued:
List-decoding, Elias-Bassalygo bound. Musing on bounds.
Reed-Solomon codes. (Notes
from 2008). Readings [Chapter
8, Chapter
5]. Scribe notes (tex,
pdf).
- Lecture 06 (Wed. 02/12): Algebra review. Reed-Solomon Codes. Extension
fields. Wozencraft ensemble. Notes from 2008 (Reed-Muller
etc., BCH).
Scribe notes (v1.tex,
v1.pdf, v2.tex, v2.pdf).
- Monday 02/17: Presidents' Day
Holiday
- Lecture 07 (Wed. 02/19):
Concatenated codes. Justesen codes. Mutltvariate
polynomials. Reed-Muller codes. Notes
from 2013. Scribe notes (tex, pdf).
- Lecture 08 (Mon. 02/24): Reed-Muller codes - some
choices of parameters. Hadamard codes, Hamming codes. BCH
codes. Scribe notes (tex,
pdf).
- Lecture 09 (Wed. 02/26): Algebraic Geometry Codes.
Decoding Reed-Solomon Codes. Reading materials.
- Lecture 10 (Mon.
03/02): Reed-Solomon decoding (contd.). Reed-Solomon
list-decoding. Scribe notes (tex,
pdf).
- Lecture 11 (Wed. 03/04): Decoding concatenated codes.
List-decoding to capacity - the question. Scribe notes (tex, pdf).
- Lecture 12 (Mon.
03/09): Folded Reed-Solomon Codes and List-decoding. Notes.
Additional Notes. Scribe
notes (tex, pdf).
- Lecture 13 (Wed. 03/11): Graph-theoretic codes
(Sipser-Spielman codes). Linear time encoding and
decoding. Notes
from 2008. No scribe notes this time, but here are
notes from previous years (tex,
pdf).
- Sat. 3/14- Sun 3/22: Spring break
- Lecture 14 (Mon.
03/23): Graph-theoretic codes I (Spielman codes). My notes. Scribe notes (tex, pdf).
- Lecture 15 (Wed. 03/25): Graph-theoretic codes II
(Alon-Luby construction, Guruswami-Indyk). Notes. Scribe notes (tex, pdf).
- Lecture 16 (Mon. 03/30): Polar codes. Introduction to
the notion. My notes. (See
also Chapter 11 from book). Scribe notes (tex, pdf).
- Lecture 17 (Wed. 04/01): Polar codes (contd):
Polarization Theorem + Algorithmic Efficiency. My notes. Scribe notes (tex, pdf).
- Lecture 18 (Mon. 04/06): Polar codes (contd): Proof of
Polarization theorem. My notes.
Scribe notes (tex, pdf).
- Lecture 19 (Wed. 04/08): Locality in coding: Definitions
of LRCs, LDCs, LTCs. Locally Recoverable Codes. My notes. Scribe notes (tex,
pdf).
- Lecture 20 (Mon. 04/13): Locality in Coding: Reed-Muller
Codes and Locality. My notes.
Scribe notes (tex, pdf).
- Lecture 21 (Wed. 04/15): Locality in Coding:
Multiplicity Codes and KMRS Codes. My notes. Scribe notes (v1.tex,
v1.pdf, v2.tex, v2.pdf).
- Lecture 22 (Mon. 04/20): Codes and derandomization:
Limited independence, epsilon-bias, almost independence. My
notes. Scribe
notes (v1.tex, v1.pdf, v2.tex, v2.pdf).
- Lecture 23 (Wed. 04/22): Coding in Complexity: Hardcore
predicates and Worst-case to average-case reductions. My notes. Scribe notes (tex, pdf).
- Lecture 24 (Mon. 04/27): Interactive Coding. My notes. Scribe
notes (v1.tex, v1.pdf, v2.tex, v2.pdf).
- Lecture 25 (Wed. 04/29): Coding for editing errors.
Course wrap-up. My notes and
slides. Scribe notes (tex, pdf).
Reference Materials: