ENEE 626: ERROR CORRECTING CODES
Graduate course for 1
st
– 2
nd
year students in EE, CS, Applied Math
Instructor :
Alexander Barg, Professor
Class times: Tuesday, Thursday 11:00am -- 12:15pm
EGR 1110
Grading: several home assignments (20%) Home
assignments (from 2015 class) Final exam [pdf] (from 2015)
Supplemental information for the course projects:
Main topics:
•
General properties of linear codes.
Matrix description, error correction, minimum distance, syndrome decoding. Bounds on codes.
Calculations with finite fields and codes are much easier with
GAP (Groups, Algorithms, and Programming). It is much better suited for manipulation of codes and computations for codes than general-purpose software such as MatLab. Gap needs to be installed locally. It has a special-purpose package to work with error correcting codes, called
Guava.
You can use GAP to check your homework papers, but unless specially stated, your solutions should be proof-based, not computer-based, and done by hand.
Sample exams:
1
2
3
4
5
6
7
8
9
10
11
12
13
Department of Electrical and Computer Engineering/Institute for Systems Research
Office: 2361 A.V.Williams Building Tel. (301) 405 7135 E-mail abarg at umd dot edu
Instructor availability outside class hours:
I am in my office most of the time: arrange to see me after class
Homepage:
http://www.ece.umd.edu/~abarg/626
class participation (20%)
course project (30%)
final (30%) (take-home exam).
No required textbook.
Lecture notes:
Part I
Part II
Part III
Part IV
Recommended reading: R. Roth, Introduction to coding theory.
J. I. Hall's lecture notes
H1
H2
H3
talk on polar codes
Papers on Turbo and LDPC decoding
Iterative decoding;
Exit Charts 1
2 ;
Design of LDPC codes
optimizer of LDPC codes
References: Ch. 3,9 in J. Hall's lecture notes, see above.
•
Random codes. Channel capacity, capacity-achieving families:
Polar codes,
LDPC codes
•
Finite fields.
Reed Solomon codes
and their decoding. List decoding algorithms (correct more errors than you can think of).
Coding for compact disks.
•
Coding for distributed storage.
References: 1. A family of codes with locality [pdf]
2. Talk on codes with local recovery [pdf]
•
Selected problems in cryptography:
Secret sharing schemes,
Wire-tap channel, Generating secret keys
References: 1. D. Stinson, An explication of secret sharing schemes
[pdf];
2. Ozarow-Wyner, Wire-tap channel
[pdf].
•
Network coding as alternative to routing: Linear network codes and capacity of multicasting
A long list of problems (some were used in the above exams).