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3 - Linear Block Codes

Published online by Cambridge University Press:  06 March 2025

William E. Ryan ,
Shu Lin  and
Stephen G. Wilson
William E. Ryan
Affiliation:
Zeta Associates
Shu Lin
Affiliation:
University of California, Davis
Stephen G. Wilson
Affiliation:
University of Virginia
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Summary

Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.

The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.

Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.

  • 300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.

  • Provides a one-stop resource for both classical and modern coding techniques.

  • Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.

  • 180 worked examples guide students through the practical application of the theory.

Type
Chapter
Information
Channel Codes
Classical and Modern
 , pp. 93 - 165
Publisher: Cambridge University Press
Print publication year: 2024

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References

Berlekamp, E. R., Algebraic Coding Theory, revised ed., Laguna Hills, CA, Aegean Park Press, 1984.Google Scholar
Blahut, R. E., Algebraic Codes for Data Transmission, Cambridge, Cambridge University Press, 2003.CrossRefGoogle Scholar
Blake, I. F. and Mullin, R. C., The Mathematical Theory of Coding, New York, Academic Press, 1975.Google Scholar
Clark, G. and Cain, J., Error-Correcting Codes for Digital Communications, New York, Plenum Press, 1981.CrossRefGoogle Scholar
Lin, S. and Costello, D. J., Jr., Error Control Coding: Fundamentals and Applications, 2nd ed., Upper Saddle River, NJ, Prentice-Hall, 2004.Google Scholar
MacWilliams, F. J. and Sloane, N. J. A., The Theory of Error-Correcting Codes, Amsterdam, North-Holland, 1977.Google Scholar
McEliece, R. J., The Theory of Information Theory and Coding, Reading, MA, Addison-Wesley, 1977.Google Scholar
Michaelson, A. M. and Levesque, A. J., Error Control Coding Techniques for Digital Communications, New York, Wiley, 1985.Google Scholar
Moreira, J. C. and Farrell, P. G., Essentials of Error-Control Coding, Chichester, Wiley, 2006.CrossRefGoogle Scholar
Peterson, W. W., “Encoding and error-correction procedures for the Bose– Chaudhuri codes,” IRE Transactions on Information Theory, vol. 6, no. 5, pp. 459–470, September 1960.CrossRefGoogle Scholar
Peterson, W. W. and Weldon, E. J., Jr., Error-Correcting Codes, 2nd ed., Cambridge, MA, MIT Press, 1972.Google Scholar
Pless, V., Introduction to the Theory of Error Correcting Codes, 3rd ed., New York, Wiley, 1998.CrossRefGoogle Scholar
Poli, A. and Huguet, L., Error Correcting Codes, Theory and Applications, Hemel Hempstead, Prentice-Hall, 1992.Google Scholar
Roth, R. M., Introduction to Coding Theory, Cambridge, Cambridge University Press, 2006.CrossRefGoogle Scholar
Wicker, S. B., Error Control Systems for Digital Communication and Storage, Englewood Cliffs, NJ, Prentice-Hall, 1995.Google Scholar
Castagnoli, G., Brauer, S., and Herrmann, M., “Optimization of cyclic redundancy-check codes with 24 and 32 parity bits,” IEEE Transactions on Communications, vol. 41, no. 6, pp. 883–892, June 1993.CrossRefGoogle Scholar
Koopman, P. and Chackravary, T., “Cyclic redundancy code (CRC) polynomial selection for embedded networks,” Proceedings of the 2004 International Conference on Dependable Systems and Networks, July 2004.CrossRefGoogle Scholar
Koopman, P., “Best CRC polynomials,” https://users.ece.cmu.edu/koopman/crc/.Google Scholar
Hocquenghem, A., “Codes correcteurs d’erreurs,” Chiffres, vol. 2, pp. 147–156, 1959.Google Scholar
Bose, R. C. and Ray-Chaudhuri, D. K., “On a class of error correcting binary group codes,” Information Control, vol. 3, pp. 68–79, March 1960.CrossRefGoogle Scholar
Massey, J. L., “Shift-register synthesis and BCH decoding,” IEEE Transactions on Information Theory, vol. 15, no. 1, pp. 122–127, January 1969.CrossRefGoogle Scholar
Chase, D., “Class of algorithms for decoding block codes with channel measurement information,” IEEE Transactions on Information Theory, vol. 18, no. 1, pp. 170–182, January 1972.CrossRefGoogle Scholar
Yang, H., Yao, H., Vardy, A., Divsalar, D., and Wesel, R., “A list-decoding approach to low-complexity soft maximum-likelihood decoding of cyclic codes,” Proceedings of the 2019 IEEE GlobeCom Conference, December 2019.CrossRefGoogle Scholar
Reed, I. S. and Solomon, G., “Polynomial codes over certain finite fields,” Journal of the Society for Industrial and Applied Mathematics, vol. 8, pp. 300–304, June 1960.Google Scholar
Sugiyama, Y., Kasahara, M., and Namekawa, T., “A method for solving key equation for decoding Goppa codes,” Information Control, vol. 27, pp. 87–99, January 1975.CrossRefGoogle Scholar
Michelson, A. and Levesque, A., Error-Control Techniques for Digital Communication, New York, Wiley, 1985.Google Scholar
Forney, G. D., “On Decoding BCH Codes,” IEEE Transactions on Information Theory, vol. 11, no. 4, pp. 549–557, October 1965.CrossRefGoogle Scholar
Forney, G. D., Jr., Concatenated Codes, Cambridge, MA, MIT Press, 1966.Google Scholar
Gronholz, B., Zeta Associates Inc., Personal Communication, May 2023.Google Scholar
Elias, P., “Error-free coding,” IRE Transactions on Information Theory, vol. 4, no. 5, pp. 29–37, September 1954.Google Scholar
Li, Z., Chen, L., Zeng, L., Lin, S., and Fong, W., “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Transactions on Communications, vol. 54, no. 1, pp. 71–81, January 2006.Google Scholar

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