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. Details Introduction to Error-Correcting Codes E C E 641 ( 3 Credits ) Description 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. Prerequisite(s) Math 320 or 340, and Math 541 or cons inst Department: ELECTRICAL AND COMPUTER ENGR College: College of Engineering Instructor Instructor Name Instructor Campus Address instructorEmail@emailaddress.edu Contact Hours 2.5 Course Coordinator N. Boston Text book, title, author, and year Alexander Barg, Course Notes, 2011. Supplemental Materials None Required / Elective / Selected Elective Selected Elective ABET Program Outcomes Associated with this Course 1 A An ability to apply knowledge of mathematics, science, and engineering 2 D An ability to function on multidisciplinary teams 3 H The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context 4 J A knowledge of contemporary issues 5 K An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice Program Specific Student Outcomes Brief List of Topics to be Covered Fundamental coding parameters: distance, packing radius. Linear codes: generator and parity check matrices, syndrome decoding, perfect codes, Hamming codes, Golay codes, self-dual codes, dual distance. Weight distributions and the MacWilliams identities, Krawtchouk polynomials. Structure of finite fields. Cyclic codes and ideals, idempotent generators. Quadratic residue codes, BCH codes, Reed-Solomon codes, Reed-Muller codes. List decoding, iterative decoding, LDPC codes, belief propagation on Tanner graph. Additional Information Printed: Dec 15, 2017 11:55:20 AM Generated by AEFIS. Developed by AEFIS, LLC Copyright © University of Wisconsin Madison 2017. All rights reserved.