Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-6bf8c574d5-685pp Total loading time: 0 Render date: 2025-03-11T17:01:40.306Z Has data issue: false hasContentIssue false

2 - Finite Fields, Vector Spaces, Finite Geometries, and Graphs

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
Get access

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. 29 - 92
Publisher: Cambridge University Press
Print publication year: 2024

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Lidl, R. and Niederreiter, H., Introduction to Finite Fields and Their Applications, revised ed., Cambridge, Cambridge University Press, 1994.Google Scholar
Blake, I. F. and Mullin, R. C., The Mathematical Theory of Coding, New York, Academic Press, 1975.Google Scholar
Carmichael, R. D., Introduction to the Theory of Groups of Finite Orders, Boston, MA, Ginn & Co., 1937.Google Scholar
Mann, H. B., Analysis and Design of Experiments, New York, Dover, 1949.Google Scholar
Tang, H., Xu, J., Lin, S., and Abdel-Ghaffar, K., “Codes on finite geometries,” IEEE Transactions on Information Theory, vol. 51, no. 2, pp. 572–596, February 2005.CrossRefGoogle Scholar
Maxfield, J. E. and Maxfield, M. W., Abstract Algebra and Solution by Radicals, New York, Dover, 1992.Google Scholar
Birkhoff, G. and MacLane, S., A Survey of Modern Algebra, New York, Macmillan, 1953.Google Scholar
Clark, A., Elements of Abstract Algebra, New York, Dover, 1984.Google Scholar
Dean, R. A., Classical Abstract Algebra, New York, Harper & Row, 1990.Google Scholar
Deo, N., Graph Theory with Applications to Engineering and Computer Science, Englewood Cliffs, NJ, Prentice-Hall, 1974.Google Scholar
Dummit, D. S. and Foote, R. M., Abstract Algebra, 3rd ed., New York, Wiley, 2004.Google Scholar
Hungerford, T. W., Abstract Algebra: An Introduction, 2nd ed., New York, Saunders College Publishing, 1997.Google Scholar
Lang, S., Algebra, 2nd ed., Reading, MA, Addison-Wesley, 1984.Google Scholar
Van der Waerden, B. L., Modern Algebra, vols. 1 and 2, New York, Ungar, 1949.Google Scholar
West, D. B., Introduction to Graph Theory, 2nd ed., Upper Saddle River, NJ, Prentice-Hall, 2001.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×