Mathematically rigorous course in error control coding fundamentals, including Bose, Ray-Chaudhuri and Hocquenghem (BCH) codes and Reed-Solomon (RS) codes, Reed-Muller codes, convolutional codes, low-density parity check (LDPC) codes. The emphasis is on decoding algorithms.

Objectives: To give the student a thorough treatment of modern error control coding principles and practice. We will discuss t he encoding and decoding algorithms for each type of code, as well as their applications and performance. After completion of the course, the student should be able to design modern coding systems, including encoders and decoders, and possess sufficient background to tackle the leading publications in the field

Class Location and Times	Elec and Comp Engr, Rm 102 Mo-We-Fr, 2-2:50PM
Instructor:	Bane Vasić, Professor Department of Electrical and Computer Engineering, 1230 East Speedway Boulevard, Room: 456P
Phone:	(520) 626-5550
Email:	vasic@ece.arizona.edu
Website:	http://www.ece.arizona.edu/~vasic
Office Hours	TBA
Textbook:	R. Roth, Introduction to Coding Theory, Cambridge University Press, 2006. J. S. Lin and D. Costello, Error Control Coding, 2nd edition, Prentice-Hall, 2004
References:	S. Wicker, Error Control Systems for Digital Communications and Storage, Prentice-Hall, 1995. S. G. Wilson, Digital Modulation and Coding, Prentice-Hall, 1995. R. Blahut, Digital Transmission of Information, Addison-Wesley, 1990. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes, North-Holland, 1977.
Credits:	ECE 635 is a three-unit, A-E based graduate course.
TA/Grader:	Xin Xiao (7xinxiao7@email.arizona.edu)

Prerequisites:	1. ECE340A (Introduction to Communications) 2. ECE330A (Computational Techniques)
Participation:	The UA’s policy concerning Class Attendance, Participation, and Administrative Drops is available at: here. The UA policy regarding absences for any sincerely held religious belief, observance or practice will be accommodated where reasonable, here . Absences pre-approved by the UA Dean of Students (or Dean Designee) will be honored. See: here. Accommodations due to the current pandemic will follow guidelines found here. Capturing video, voice, screen, and any other content of lectures, discussions, students, participants, etc. in any form is not permitted
Student Questions:	The instructor will not be able to answer questions submitted by e-mail or phone, nor to accept student visits out of the office hours.
Projects and Homework	There will be no homework in this class, i.e., homework if assigned will be graded as a reference to the final grade. Solved problems will be posted on the instructor’s web page. There will be at most four medium size computer projects instead.
Exams:	There will be two mid-term exams.       midterm1 October 5       midterm2 November 9 The final exam schedule can be found here. Exams will include material/topics discussed in class. The final exam is mandatory.
Computer Problems:	These will be integrated with your regular homework. Students may use any convenient math software.
Grading Policy:	Graded work includes exams and projects. Final grades will be determined by your total number of points compared to an absolute scale. The course grade will be percentage based and I guarantee the following minimum cutoffs for grades:       Percentage Grade       >90% A       >80% B       >70% C       >60% D The weights below will be used to determine your point total and your final grade:       Projects 40%       Midterms 40%       Final 20%
Academic Integrity:	Students are encouraged to share intellectual views and discuss freely the principles and applications of course materials. However, graded work/exercises must be the product of independent effort unless otherwise instructed. Students are expected to adhere to the UA Code of Academic Integrity as described in the UA General Catalog. See: here. The University Libraries have some excellent tips for avoiding plagiarism available at: here. Selling class notes and/or other course materials to other students or to a third party for resale is not permitted without the instructor’s express written consent. Violations to this and other course rules are subject to the Code of Academic Integrity and may result in course sanctions. Additionally, students who use D2L or UA email to sell or buy these copyrighted materials are subject to Code of Conduct Violations for misuse of student email addresses. This conduct may also constitute copyright infringement.
UA Nondiscrimination and Anti-Harassment Policy	The University is committed to creating and maintaining an environment free of discrimination, here.
Subject to Change Statement:	Information contained in the course syllabus, other than the grade and absence policy, may be subject to change with advance notice, as deemed appropriate by the instructor.

Overview of channel coding: Information theory and Shannon channel coding theorem.
Galois fields: Groups, fields, and vector spaces. Polynomials over Galois fields.
Linear block codes: Block codes, linear block codes, generator and parity check matrices, weight distributions, cyclic codes.
Important classes of linear block codes: Hamming codes, Hadamard codes, Golay codes, Reed-Muller codes.
Reed-Muller codes: Constructions of Reed-Muller codes. The Reed decoding algorithm.
Bose, Ray-Chaudhuri and Hocquenghem (BCH) codes and Reed-Solomon (RS) codes: Generator polynomials of BCH and RS codes. Decoding algorithms. Erasure decoding.
Convolutional codes: Viterbi algorithm. Soft output Viterbi (SOVA) algorithm. Bahl, Cocke, Jelinek and Raviv (BCJR) algorithm.
Codes on graphs: Low-density parity check (LDPC) codes, quasi-cyclic LDPC codes, code constructions.
Iterative decoding of codes on graphs: Gallager A and B algorithms, Belief propagation, failures of iterative decoders - stopping and trapping sets.