Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 641: Introduction to Error-Correcting Codes

Frequency: 

Irregular

Student Body: 

Math, Comp Sci, Stat and Elec Eng advanced undergraduate and graduate students

Background and Goals: 

Math/ECE 641 is a first course on coding theory with emphasis on linear codes and covering the basics of the subject. It is essential that the student have a good knowledge of basic linear algebra; some knowledge of abstract algebraic systems (finite fields, polynomial rings and ideals, ...) is very helpful. We shall have to develop some of the theory of finite fields. This is necessary even if one is only interested in binary codes.

Alternatives: 

n/a

Subsequent Courses: 

n/a

 
Course Content:
 
Coding theory is the efficient use of redundancy to ensure the correction of errors in data transmission. It is a marvelous application of clever uses of algebra and combinatorics to problems of practical importance (satellite imagery, scratched CD's). We will follow Barg's excellent course notes - covering topics such as linear codes, Reed-Solomon codes, list decoding, cyclic codes, ensembles of random codes, iterative decoding, belief propagation, and LDPC codes, culminating in describing capacity - achieving codes for the binary erasure channel, which answers a basic question posed by Shannon 60 years ago.
 
In order to construct and investigate codes, we will have to develop finite fields sufficiently to get a good computational understanding of their construction, arithmetic, and algebra.
credits: 
3 (N-A)
semester: 
InFrequent
prereqs: 
Math 320 or 340; and Math 541 or consent of instructor.

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, Wi  53706

(608) 263-3054

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