Discrete Mathematics II
MA533/CS525D: Topics in Coding Theory
Mondays 5:30--8:20 p.m. Spring 2015
Office Hours: Thursdays and Fridays 2-3pm
Last modified: February 9, 2015
This course explores a variety of cutting edge topics in
coding theory and communications, with a focus on emerging
combinatorial problems.
"Algebraic coding theory" deals with techniques for adding redundancy to
messages in communications in order to recover the original message even
in the event that part of the signal is lost or corrupted. This confluence
of electrical engineering, computer science and mathematics has seen great
success. Error-correcting codes have played a key role in space communications,
packet transmission over digital networks, cellphone protocols, and digital
storage schemes.
The course begins with a brief introduction to this theory, which developed
significantly during the 1960s and 1970s. We will look at some of the more
interesting decoding algorithms used in practice. Then we will move on to
current topics and new challenges in coding theory. As time permits, we will
discuss:
- decoding algorithms
- linear programming and semidefinite programming bounds
- quantum error-correcting codes
- low-density parity check codes
- network coding
- large storage facilities
- polar codes
The lists below itemize course material, some background references, books and papers
relevant to our course curriculum, and links to various uses of coding theory as well
as anecdotes that I think the students might find interesting.
Course Material
Background Material
- Short article
on error-correcting codes at the American Mathematical Society (AMS)
- Contemporary Abstract Algebra by Joseph Gallian
-
short tutorial on finite fields by Professor Keith Conrad, UConn. (Prof. Conrad provides
many more expository papers on algebraic topics
here.
Primary Sources
Anecdotes, Applications of Coding Theory
William J. Martin / WPI
/ martin.deletethis@wpi.edu