University of Toronto
Department of Electrical & Computer Engineering

ECE 1501, Winter 2007

Error Control Codes

Instructor:	F. R. Kschischang, BA 4132
E-mail:	frankcommutorontoca
Lectures:	Tuesdays, 10:30am-12:00pm, BA 2139 Fridays, 2:00pm-3:30pm, BA 4164 Lectures commence on Tuesday, January 9, 2007

This course is an introduction to error control coding. The field of error control coding is aimed at devising efficient encoding and decoding procedures to achieve reliable transmission of information across channels which are corrupted by noise. Elwyn Berlekamp's observation in the preface to his classic 1968 text Algebraic Coding Theory is as true today as it was then:

From a practical standpoint, the essential limitation of all coding and decoding schemes proposed to date has not been Shannon's capacity but the complexity (and cost) of the decoder. For this reason, efforts have been directed toward the design of coding and decoding schemes which could be easily implemented.

Algebraic Decoding:

discrete channels and hard-decision decoding, algebraic coding theory: finite fields, linear block codes and their basic properties, cyclic codes, BCH codes and decoding, Reed-Solomon codes.

Trellis Decoding:

channel and soft-decision decoding, the Viterbi algorithm, trellis structure of codes, convolutional codes, trellis-coded modulation.

Iterative Decoding:

codes defined on graphs, the sum-product algorithm, soft-output decoding, low-density parity-check codes, turbo codes.

There is no official textbook; however, you may wish to refer to the references listed below.

Other References:

1. R. M. Roth, Introduction to Coding Theory, Cambridge University Press, 2006.
2. T. K. Moon, Error Correction Coding: Mathematical Methods and Algorithms, Wiley 2005.
3. S. Ling and C. Xing, Coding Theory, A First Course, Cambridge University Press, 2004.
4. D. J. C. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press, 2003.
5. S. B. Wicker, Error Control Systems for Digital Communication and Storage, Prentice-Hall, 1995.
   
6. S. G. Wilson, Digital Modulation and Coding, Prentice-Hall, 1996.
   
7. R. J. McEliece, Finite Fields for Computer Scientists and Engineers, Kluwer Academic Publishers, 1987.
8. R. E. Blahut, Theory and Practice of Error Control Codes, Addison-Wesley, 1983.
   
9. S. Lin and D. J. Costello, Jr., Error Control Coding: Fundamentals and Applications, Prentice-Hall, 1983.
   
10. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1978.
    
11. W. W. Peterson and E. J. Weldon, Jr., Error-Correcting Codes, MIT Press, 1972.
    
12. E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, 1968.
    

Web Resources:

1. Victor Shoup's NTL (number theory library).
2. Arash Partow's Galois field arithmetic C++ library.

Grading:

Grades will be determined on the basis of five problem sets (40%), a survey paper or project (25%), and a final examination (35%).