520.460 Error Control Coding
Fall, 2007

A. Brinton Cooper III (abcooper@jhu.edu)

Prerequisites: Linear Algeba; Probability

Class Schedule: MTW, 11:00-11:50, 225 Barton

Text:

• Essentials of Error-Control Coding, Jorge Castiñeira Moreira and Patrick G. Farrell, John Wiley & Sons, Ltd, 2006 (Required)

Other references:

Codiing has matured nicely over the last two decades, and many fine references are available.  A few  are listed below
for your interest,  but you need only Moreira and Farrell for the course.

• Shu Lin and Daniel J. Costello, Error Control Coding,  Prentice Hall, 2004
• R. McEliece, The Theory of Information and Coding, Student Edition,  Cambridge, 2004
• S.B. Wicker, Error Control Systems for Digital Communication and Storage,  Prentice-Hall 1995
• E.R. Berlekamp, Algebraic Coding Theory (rev. ed.), Aegean Park Press, Laguna Hills, 1984.
• R.E. Blahut, Algebraic Codes for Data Transmission, Cambridge University Press, Cambridge, UK, 2003.
• M. Bossert, Channel Coding for Telecommunications, Wiley, 2000.
• P. Sweeney, Error Control Coding:  An Introduction, Prentice-Hall, 1991.
• J. MacWilliams and N.J.A. Sloane, The Theory of Error Correcting Codes, North-Holland, Amsterdam, 1977 (out of print; occasionally in two volumes).
• A.M. Michelson and A.H. Levesque, Error-Control Techniques for Digital Communication, Wiley, New York, 1985.
• W.W. Peterson and E.J. Weldon, Error-Correcting Codes (2nd ed.), MIT Press, Cambridge, MA, 1972.

Syllabus:

1. Introduction:
• Reason for coding. Performance
• Introduction to algebra
• Construction of finite fields
• Linear block codes
2. Cyclic codes
• Description; generator and parity check matrices; encoding
• Syndromes and error detection
• Binary BCH codes:  generation and properties
• Decoding binary BCH codes
3. Nonbinary cyclic codes
• q-ary linear block codes; Reed-Solomon codes
• Berlekamp's decoding algorithm
• Euclidean decoding algorithm
4. Probabilistic coding
• Convolutional codes:  encoding, structural, and distance properties
• Viterbi decoding
• MAP decoding
5. Capacity-approaching codes
• The turbo principle; design of turbo codes
• Iterative decoding of turbo codes
• LDPC codes; introduction, graph representation
• sum-product algorithm

Course management:

• Exercise problems at the end of each chapter will be suggested.  Answers to the problems appear at the end of the book for (nearly) all problems.  Therefore, they will not be collected or graded.  If you cannot get the book's answer to a problem after working hard on it, send me e-mail.  If the problem is of general interest, we will discuss it in class.  Otherwise, you and I will work privately on it.
• The final grade will be based on two mid-term exams and one final.  The final will count as 40% of the grade.

Ethics:

• The JHU Undergraduate Ethics Policy is found here.
• For this course, there will be no
• collaboration on exams, quizzes, or homeworks
• direct copying of any assignment from any source
• interference with any student's work

Discussions:

• I am available for discussions whenever my door (210 Barton Hall) is open, usually most of the day Mon-Wed.
• Otherwise contact me by e-mail to arrange a meeting time.

Notes:

• Cyclic codes
• Intro to BCH and RS codes
• Solving the Key Equation for RS Codes
• Convolutional  Codes
• VA Performance on the BSC
• MAP Decoding
•  LDPC  Codes (11.29.07)

still a work in progress...

 "If your (communications) system doesn't use coding, it's probably over-designed," Elwyn R. Berlekamp, "The Technology of Error-Correcting Codes," Proceedings of the IEEE, 1980.