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4 - Convolutional 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. 166 - 234
Publisher: Cambridge University Press
Print publication year: 2024

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References

Elias, P., “Coding for noisy channels,” IRE Convention Record, vol. 3, no. 4 pp. 37–47, 1955.Google Scholar
Forney, G. D., Jr., “Convolutional codes I: Algebraic structure,” IEEE Transactions on Information Theory, vol. 16, no. 11, pp. 720–738, November 1970.CrossRefGoogle Scholar
Johannesson, R. and Zigangirov, K., Fundamentals of Convolutional Coding, New York, IEEE Press, 1999.CrossRefGoogle Scholar
Viterbi, A. J., “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm,” IEEE Transactions on Information Theory, vol. 13, no. 4, pp. 260–269, April 1967.CrossRefGoogle Scholar
Forney, G. D., Jr., “The Viterbi algorithm,” Proceedings of the IEEE, pp. 268–278, March 1973.Google Scholar
Bahl, L., Cocke, J., Jelinek, F., and Raviv, J., “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Transactions on Information Theory, vol. 20, no. 3, pp. 284–287, March 1974.CrossRefGoogle Scholar
Seshadri, N. and Sundberg, C-E., “List Viterbi decoding algorithms with applications,” IEEE Transactions on Communications, pp. 313–323, February–April 1994.CrossRefGoogle Scholar
Shao, R., Lin, S., and Fossorier, M., “Two decoding algorithms for tailbiting codes,” IEEE Transactions on Communications, vol. 51, no. 10, pp. 1658–1665, October 2003.Google Scholar
Fano, R. M., “A heuristic discussion of probabilistic decoding,” IEEE Transactions on Information Theory, pp. 64–74, April 1963.CrossRefGoogle Scholar
Viterbi, A. J., “Convolutional codes and their performance in communication systems,” IEEE Transactions on Communication Technology, vol. 19, no. 5, pp. 751–772, October 1971.CrossRefGoogle Scholar
Oppenheim, A. V. and Schafer, R. W., Discrete-Time Signal Processing, Englewood Cliffs, NJ, Prentice-Hall, 1989.Google Scholar
Lin, S. and Costello, D. J., Jr., Error Control Coding, 2nd ed., New Saddle River, NJ, Prentice-Hall, 2004.Google Scholar
Wicker, S., Error Control Systems for Digital Communication and Storage, Englewood Cliffs, NJ, Prentice-Hall, 1995.Google Scholar
Lou, C.-Y., Daneshrad, B., and Wesel, R. D., “Convolutional-code-specific CRC code design,” IEEE Transactions on Communications, vol. 63, no. 10, pp. 3459–3470, October 2015.CrossRefGoogle Scholar
Yang, H., Liang, E., Pan, M., and Wesel, R. D., “CRC-aided list decoding of convolutional codes in the short blocklength regime,” IEEE Transactions on Information Theory, vol. 68, no. 6, pp. 3744–3766, June 2022.CrossRefGoogle Scholar
Baldauf, A., Belhouchat, A., Kalantarmoradian, S., Sung-Miller, A., Song, D., Wong, N., and Wesel, R. D., “Efficient computation of Viterbi decoder reliability with an application to variable-length coding,” IEEE Transactions on Communications, vol. 70, no. 9, pp. 5711–5723, September 2022.CrossRefGoogle Scholar
Schiavone, R., Garello, R., and Liva, G., “Performance improvement of space missions using convolutional codes by CRC-aided list Viterbi algorithms,” IEEE Access, vol. 11, pp. 55925–55937, June 2023.CrossRefGoogle Scholar
Hulse, C., “FPGA implementation of decoders for CRC-aided tail-biting convolutional codes,” Master’s thesis, ECE Department, UCLA, 2022.Google Scholar
King, J., Ryan, W. E., and Wesel, R., “Efficient maximum-likelihood decoding for TBCC and CRC-TBCC codes via parallel list Viterbi,” 2023 International Symposium on Topics in Coding.Google Scholar
Fossorier, M. and Lin, S., “Differential trellis decoding of convolutional codes,” IEEE Transactions on Information Theory, vol. 46, no. 5, pp. 1046–1053, May 2000.Google Scholar
Massey, J. L., “Variable-length codes and the Fano metric,” IEEE Transactions on Information Theory, pp. 196–198, January 1972.CrossRefGoogle Scholar
Wozencraft, J. M. and Jacobs, I. M., Principles of Communication Engineering, Chichester, Wiley, 1965.Google Scholar
Robertson, P., Villebrun, E., and Hoeher, P., “A comparison of optimal and suboptimal MAP decoding algorithms operating in the log domain,” Proceedings of the 1995 International Conference on Communications, pp. 1009–1013.Google Scholar
Anderson, J. B. and Hladik, S. M., “Tailbiting MAP decoders,” IEEE Journal on Selected Areas in Communications, vol. 16, no. 2, pp. 297–302, February 1998.CrossRefGoogle Scholar
Coșkun, M., Durisi, G., Jerkovits, T., Liva, G., Ryan, W., Stein, B., and Steiner, F., “Efficient error-correcting codes in the short blocklength regime,” Physical Communication, vol. 34, pp. 66–79, June 2019.Google Scholar
Robertson, P., Villebrun, E., and Hoeher, P., “A comparison of optimal and suboptimal MAP decoding algorithms operating in the log domain,” Proceedings of the 1995 International Conference on Communications, November 1999, pp. 317–319.Google Scholar

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