ECE 641: Introduction to Error-Correcting Codes

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ECE 641 - Introduction to Error-Correcting Codes

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ECE 641 Introduction to Error-Correcting Codes, Fall09 (1) Sections: 001

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Catalog Description

641 Introduction to Error-Correcting Codes. (Crosslisted with Math) Irr; 3 cr (N-A). A first course in coding theory. Linear codes, decoding and encoding. Hamming codes, Shannon's theorem on the existence of good codes. The binary Golay code. Finite fields and BCH codes. Dual codes and the weight distribution. Cyclic codes: generator polynomial and check polynomial. Reed-Solomon codes and burst errors. The Euclidean algorithm for decoding BCH codes. Reed-Muller codes. P: Math 320 or 340; and Math 541 or cons inst.

Course Prerequisite(s)

Math 320
Math 340
Math 541

Prerequisite knowledge and/or skills

Elementary linear algebra
Finite fields
Elementary probability

Textbook(s) and/or other required material

The course is largely based on class notes.

Course objectives

This course is designed to introduce the student to error- correcting codes, their construction and properties, encoding and decoding.

Topics covered

Entropy and source coding: uniquely decodable codes, prefix codes
The idea of an error-correcting code and Shannon's fundamental channel coding theorem
Fundamental coding parameters: distance, packing radius, covering radius
Linear codes: generator and parity check matrices, syndrome decoding, perfect codes, Hamming codes, Golay codes, self-dual codes, dual distance
Structure of finite fields
Cyclic codes and ideals, idempotent generators
Quadratic residue codes, BCH codes, Reed-Solomon codes
Weight distributions and the MacWilliams identities, Krawtchouk polynomials
Reed-Muller codes

Class/laboratory schedule

Three 50-minute lectures or two 75-minute lectures per week.

Contribution of course to meeting the professional component

This course contributes primarily to the students' knowledge of engineering topics, but does not provide design experience.

The following statement indicates which of the following considerations are included in this course: economic, environmental, ethical, political, societal, health and safety, manufacturability, sustainability.

manufacturability

Relationship of course to undergraduate degree program objectives and outcomes

This course primarily serves students in the department. The information below describes how the course contributes to the undergraduate program objectives.

developing advanced expertise in design, analysis, and fabrication techniques within a student-selected electrical and computer engineering concentration area

Assessment of student progress toward course objectives

weekly homework assignments
midterm exams
final exam
projects

Person(s) who prepared this description

Daniel Cobb

Copyright 2007 The Board of Regents of the University of Wisconsin System
Date last modified: 18-Jul-2007
Content by: ece@engr.wisc.edu
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