Book contents
- Channel Codes
- Channel Codes
- Copyright page
- Dedication
- Contents
- Detailed Contents
- Preface to the Second Edition
- Acknowledgments (Second Edition)
- Preface to the First Edition
- Acknowledgments (First Edition)
- 1 Coding and Capacity
- 2 Finite Fields, Vector Spaces, Finite Geometries, and Graphs
- 3 Linear Block Codes
- 4 Convolutional Codes
- 5 Low-Density Parity-Check Codes
- 6 Computer-Based Design of LDPC Codes
- 7 Turbo Codes
- 8 Ensemble Enumerators for Turbo and LDPC Codes
- 9 Ensemble Decoding Thresholds for LDPC and Turbo Codes
- 10 Polar Codes
- 11 Finite-Geometry LDPC Codes
- 12 Constructions of LDPC Codes Based on Finite Fields
- 13 LDPC Codes Based on Combinatorial Designs, Graphs, and Superposition
- 14 LDPC Codes for Binary Erasure Channels
- 15 Nonbinary LDPC Codes
- Index
- References
5 - Low-Density Parity-Check Codes
Published online by Cambridge University Press: 06 March 2025
Book contents
- Channel Codes
- Channel Codes
- Copyright page
- Dedication
- Contents
- Detailed Contents
- Preface to the Second Edition
- Acknowledgments (Second Edition)
- Preface to the First Edition
- Acknowledgments (First Edition)
- 1 Coding and Capacity
- 2 Finite Fields, Vector Spaces, Finite Geometries, and Graphs
- 3 Linear Block Codes
- 4 Convolutional Codes
- 5 Low-Density Parity-Check Codes
- 6 Computer-Based Design of LDPC Codes
- 7 Turbo Codes
- 8 Ensemble Enumerators for Turbo and LDPC Codes
- 9 Ensemble Decoding Thresholds for LDPC and Turbo Codes
- 10 Polar Codes
- 11 Finite-Geometry LDPC Codes
- 12 Constructions of LDPC Codes Based on Finite Fields
- 13 LDPC Codes Based on Combinatorial Designs, Graphs, and Superposition
- 14 LDPC Codes for Binary Erasure Channels
- 15 Nonbinary LDPC Codes
- Index
- References
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 CodesClassical and Modern, pp. 235 - 280Publisher: Cambridge University PressPrint publication year: 2024
References
Gallager, R. G., Low-Density Parity-Check Codes, Cambridge, MA, MIT Press, 1963. (Also, Gallager, R. G., “Low density parity-check codes,” IRE Transactions on Information Theory, vol. 8, no. 1, pp. 21–28, January 1962.)CrossRefGoogle Scholar
Tanner, R. M., “A recursive approach to low complexity codes,” IEEE Transactions on Information Theory, vol. 27, no. 9, pp. 533–547, September 1981.CrossRefGoogle Scholar
MacKay, D. and Neal, R., “Good codes based on very sparse matrices,” Cryptography and Coding, 5th IMA Conference, Boyd, C., (Ed.), Berlin, Springer-Verlag, October 1995.Google Scholar
MacKay, D., “Good error correcting codes based on very sparse matrices,” IEEE Transactions on Information Theory, vol. 45, no. 3, pp. 399–431, March 1999.CrossRefGoogle Scholar
Alon, N. and Luby, M., “A linear time erasure-resilient code with nearly optimal recovery,” IEEE Transactions on Information Theory, vol. 42, no. 11, pp. 1732–1736, November 1996.CrossRefGoogle Scholar
Byers, J., Luby, M., Mitzenmacher, M., and Rege, A., “A digital fountain approach to reliable distribution of bulk data,” ACM SIGCOMM Computer Communication Review, vol. 28, issue 4, October 1998.CrossRefGoogle Scholar
Pearl, J., Probabilistic Reasoning in Intelligent Systems, San Mateo, CA, Morgan Kaufmann, 1988.Google Scholar
Wang, Y. and Fossorier, M., “Doubly generalized LDPC codes,” 2006 IEEE International Symposium on Information Theory, July 2006, pp. 669–673.CrossRefGoogle Scholar
Kschischang, F., Frey, B., and Loeliger, H.-A., “Factor graphs and the sum-product algorithm,” IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 498–519, February 2001.CrossRefGoogle Scholar
Jones, C., Valles, E., Smith, M., and Villasenor, J., “Approximate-min* constraint node updating for LDPC code decoding,” IEEE Military Communications Conference, October 2003, pp. 157–162.Google Scholar
Jones, C., Dolinar, S., Andrews, K., Divsalar, D., Zhang, Y., and Ryan, W., “Functions and architectures for LDPC decoding,” 2007 Information Theory Workshop, pp. 577–583, September 2007.Google Scholar
Zhang, Y., Design of Low-Floor Quasi-Cyclic IRA Codes and their FPGA Decoders, PhD thesis, ECE Department, University of Arizona, May 2007.Google Scholar
Zhang, Y. and Ryan, W. E., “Toward low LDPC-code floors: A case study,” IEEE Transactions on Communications, pp. 1566–1573, June 2009.CrossRefGoogle Scholar
Han, Y. and Ryan, W. E., “Low-floor decoders for LDPC codes,” IEEE Transactions on Communications, pp. 1663–1673, June 2009.CrossRefGoogle Scholar
Butler, B. and Siegel, P., “Error floor approximation for LDPC code in the AWGN channel,” IEEE Transactions on Information Theory, vol. 60, no. 12, pp. 7416–7441, December 2014.CrossRefGoogle Scholar
Zhao, J., Zarkeshvari, F., and Banihashemi, A., “On implementation of min-sum algorithm and its modifications for decoding low-density parity-check (LDPC) codes,” IEEE Transactions on Communications, vol. 53, no. 4, pp. 549–554, April 2005.CrossRefGoogle Scholar
Chen, J., Dholakia, A., Eleftheriou, E., Fossorier, M., and Hu, X.-Y., “Reduced-complexity decoding of LDPC codes,” IEEE Transactions on Communications, vol. 53, no. 8, pp. 1288–1299, August 2005.Google Scholar
Zhang, Z., Dolecek, L., Nikolic, B., Anantharam, V., and Wainwright, M., “Lowering LDPC error floors by postprocessing,” 2008 IEEE GlobeCom Conference, November–December 2008, pp. 1–6.Google Scholar
Hu, X.-Y., Eleftheriou, E., Arnold, D.-M., and Dholakia, A., “Efficient implementation of the sum–product algorithm for decoding LDPC codes,” proceedings of the 2001 IEEE GlobeCom Conference, November 2001, pp. 1036–1036E.Google Scholar
Li, Z.-W., Chen, L., Zeng, L.-Q., 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
Miles, L. H., Gambles, J. W., Maki, G. K., Ryan, W. E., and Whitaker, S. R., “An 860-Mb/s (8158, 7136) low-density parity-check encoder,” IEEE Journal of Solid-State Circuits, pp. 1686–1691, August 2006.Google Scholar
Huang, X., “Single-scan min-sum algorithms for fast decoding of LDPC codes,” IEEE Information Theory Workshop, Chengdu, China, September 2006.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.Google Scholar
McEliece, R., “On the BCJR trellis for linear block codes,” IEEE Transactions on Information Theory, vol. 42, no. 7, pp. 1072–1092, July 1996.Google Scholar
Ardakani, M., Efficient Analysis, Design and Decoding of Low-Density Parity-Check Codes, PhD thesis, University of Toronto, 2004.Google Scholar
Xiao, H. and Banihashemi, A. H., “Graph-based message-passing schedules for decoding LDPC codes,” IEEE Transactions on Communications, vol. 52, no. 12, pp. 2098–2105, December 2004.Google Scholar
Vila Casado, A., Griot, M., and Wesel, R. D., “Informed scheduling for belief-propagation decoding of LDPC codes,” 2007 International Conference on Communications, June 2007, pp. 932–937.CrossRefGoogle Scholar
Mansour, M. and Shanbhag, N., “High-throughput LDPC decoders,” IEEE Transactions on VLSI Systems, pp. 976–996, December 2003.Google Scholar
Chen, J. and Fossorier, M., “Near optimum universal belief propagation based decoding of low-density parity check codes,” IEEE Transactions on Communications, vol. 50, no. 3, pp. 406–414, March 2002.CrossRefGoogle Scholar
Chen, J., Dholakia, A., Eleftheriou, E., Fossorier, M., and Hu, X.-Y. “Reduced-complexity decoding of LDPC codes,” IEEE Transactions on Communications, vol. 53, no. 8, pp. 1288–1299, August 2005.Google Scholar
Fossorier, M., “Iterative reliability-based decoding of low-density parity check codes,” IEEE Journal on Selected Areas in Communications, vol. 19, no. 5, pp. 908–917, May 2001.CrossRefGoogle Scholar
Kou, Y., Lin, S., and Fossorier, M., “Low-density parity-check codes based on finite geometries: a rediscovery and new results,” IEEE Transactions on Information Theory, vol. 47, no. 11, pp. 2711–2736, November 2001.Google Scholar
Lin, S. and Costello, D. J., Jr., Error Control Coding &, 2nd edn., New Saddle River, NJ, Prentice-Hall, 2004.Google Scholar