University of Wisconsin Madison
Introduction to Error-Correcting Codes (E C E 641) Syllabus
Course Learning Outcomes
    Course Learning Outcome
  • 1
    Students will be able to implement classical coding and decoding schemes.
  • 2
    Students will be able to use ubiquitous codes such as the Reed-Solomon codes and variants, having learned the finite field theory underlying them.
  • 3
    Students will be able to understand and carry out iterative decoding of low ensity parity check codes.
Introduction to Error-Correcting Codes
E C E 641 ( 3 Credits )
A first course in coding theory. Codes (linear, Hamming, Golay, dual); decoding-encoding; Shannon's theorem; sphere-packing; singleton and Gilbert-Varshamov bounds; weight enumerators; MacWilliams identities; finite fields; other codes (Reed-Muller, cyclic, BCH, Reed-Solomon) and error-correction algorithms.
Math 320 or 340, and Math 541 or cons inst
College: College of Engineering
Instructor Name
Instructor Campus Address
Contact Hours
Course Coordinator
N. Boston
Text book, title, author, and year
Alexander Barg, Course Notes, 2011.
Supplemental Materials
Required / Elective / Selected Elective
Selected Elective
ABET Program Outcomes Associated with this Course
Program Specific Student Outcomes
Brief List of Topics to be Covered
  1. Fundamental coding parameters: distance, packing radius.
  2. Linear codes: generator and parity check matrices, syndrome decoding, perfect codes, Hamming codes, Golay codes, self-dual codes, dual distance.
  3. Weight distributions and the MacWilliams identities, Krawtchouk polynomials.
  4. Structure of finite fields.
  5. Cyclic codes and ideals, idempotent generators.
  6. Quadratic residue codes, BCH codes, Reed-Solomon codes, Reed-Muller codes.
  7. List decoding, iterative decoding, LDPC codes, belief propagation on Tanner graph.
Additional Information
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