General Info:
- Lecturer:
Madhu
Sudan; MD 339; email: first name at cs dot
harvard dot edu; Office Hours: TuTh 5-6pm (tentative)
- Lecture Time and Location: TuTh
11:30am-1:00pm in Cruft 309.
Other links for the course:
Announcements:
- LECTURE on 02/09/17 CANCELLED!!
- Please sign up for scribing! Signup instructions and
sheet here. Template for
scribing here (preamble,
lect01.tex).
- Problem Set 1 (tex, pdf). Due Wednesday 02/08/2017.
Canvas
link.
- Problem Set 2 (tex, pdf). Due Wednesday 2/22/2017.
Canvas
link.
- Problem Set 3 (tex, pdf). Due Wednesday 3/8/2017. Canvas
link.
- Here
is a list of potential projects (or you can suggest your
own idea). I will email the editable link and you can edit
the sheet to express interest in a project. If you don't
have a partner in mind, it might be good to trawl the
sheet for a combination of project+partner.
- PROJECTS + PRESENTATIONS: Schedule here.
All presentations will be held in MD 323 on Tuesday, May
2, 2017.
Topics (Tentative), Calendar
and Handouts:
- Lecture 01 (Tue. 01/24): Introduction. Hamming's Paper.
Codes, Distance, Examples, Limits and Algorithms. Notes from 2008 (use these
notes for technical content; not for grading policy
etc.!). Scribe Notes (tex,
pdf). Reading [Chapter
1 and Chapter
2 from the text.]
- Lecture 02 (Thu. 01/26): Shannon's Theorems. Noiseless
coding. Noisy Coding. Shannon Capacity. Notes from 2008. Reading [Chapter
6]. Scribe notes (tex,
pdf).
- Lecture 03 (Tue. 01/31): 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 (Thu. 02/02): Simple Impossibility Results
for Codes. (Pigeonhole argument, packing argument,
geometric arguments). Reading [Chapter
4 and Chapter
8]. Notes from 2008, Scribed
notes from 2001. Scribe notes (tex, pdf).
- Lecture 05 (Tue. 02/07): Finish impossibility results. (Notes from 2008). Algebraic
codes: Reed-Solomon codes. Concatenated codes. (Notes from 2008). Readings [Chapter
8, Chapter
5]. Scribe notes (tex,
pdf).
- Lecture 06 (Thu. 02/09): LECTURE CANCELLED due to
weather.
- Lecture 07 (Tue. 02/14): Codes from univariate
polynomials contd.: Forney, Justesen. BCH codes. Codes
from Multivariate polynomials: Reed-Muller, Hadamard.
Notes from 2008 (Reed-Muller
etc., BCH).
Scribe notes (tex, pdf).
- Lecture 08 (Thu. 02/16): Dual BCH codes. Algebraic
Geometry Codes. Notes
from 2013. Scribe notes (tex,
pdf).
- Monday 02/20: Presidents' Day
Holiday
- Lecture 09 (Tue. 02/21): Algorithmic problems in Coding
theory. Decoding Reed-Solomon Codes. Reading materials.
- Lecture 10 (Thu. 02/23): Decoding Concatenated Codes.
Achieving Shannon Capacity. Notes
from 2008. Scribe notes (tex,
pdf).
- Lecture 11 (Tue. 02/28): List-decoding: Combinatorics.
List-decoding Reed-Solomon Codes. Notes
from 2008. Scribe notes (tex,
pdf).
- Lecture 12 (Thu. 03/02): Folded Reed-Solomon Codes and
List-decoding. Notes. No
scribe notes, but the notes from 2013 should be pretty
close to what we did (tex,
pdf).
- Lecture 13 (Tue. 03/07): Graph-theoretic codes
(Gallager, Tanner, Sipser-Spielman). Linear time encoding
and decoding. Notes
from 2008. Scribe notes (tex,
pdf).
- Lecture 14 (Thu. 03/09): Graph-theoretic codes II
(Alon-Luby construction, Guruswami-Indyk). Notes. Scribe notes (tex, pdf).
- Sat. 3/11- Sun 3/19: Spring break
- Lecture 15 (Tue. 03/21): Polar codes. Introduction to
the notion. Encoding + Decoding. References:
- Lecture 16 (Thu. 03/23): Polar codes. Shannon capacity
with polynomial convergence. Notes.
Scribe notes (tex, pdf).
- Lecture 17 (Tue. 03/28): CANCELLED.
- Lecture 18 (Thu. 03/30): Locality in coding:
Introduction, Locally Recoverable Codes. Notes. Scribe notes (tex, pdf).
- Lecture 19 (Tue. 04/04): Locality in coding: Locally
Decodable Codes. Notes.
Scribe notes (tex, pdf).
- Lecture 20 (Thu. 04/06): Locality in Coding: Locally
Testable Codes. Notes.
- Lecture 21 (Tue. 04/11): Local Testability of Tensor
Products and Low-degree polynomials. Notes.
- Lecture 22 (Thu. 04/13): Codes and derandomization:
Limited independence, epsilon-bias, almost independence. Notes.
- Lecture on Tue 04/18 Guest Lecture
by Pritish Kamath. Interactive Coding - I. My notes (part I and part II).
- Lecture on Tue 04/20 Guest Lecture
by Pritish Kamath. Interactive Coding - II. Pritish's Notes.
- Lecture 23 (Tue. 04/25): (Last lecture) Codes and
complexity: Pseudorandom generation from one-way
functions, Hardness amplification. Notes. Scribe notes (tex, pdf).
Reference Materials: