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-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-19T13:20:55.551Z Has data issue: false hasContentIssue false

4 - Information theory and channel coding

Published online by Cambridge University Press:  05 June 2012

Tri T. Ha
Tri T. Ha
Affiliation:
Naval Postgraduate School, Monterey, California
Get access

Summary

Introduction

In this chapter we present the applicability of probability theory and random variables to the formulation of information theory pioneered by Claude Shannon in the late 1940s. Information theory introduces the general idea of source coding and channel coding. The purpose of source coding is to minimize the bit rate required to represent the source (represented mathematically by a discrete random variable) with a specified efficiency at the output of the source coder. On the other hand, the goal of channel coding is to maximize the bit rate at the input of the channel encoder so that code words can be transmitted through the channel with a specified reliability. Both source coding and channel coding can be achieved with the knowledge of the statistics of both the source and channel.

Entropy of a discrete source

Information comes from observing the outcome of an event. Common events occur frequently (high probability) and therefore carry little information. On the other hand, rare events occur infrequently (low probability) and hence carry much more information. In 1928 R. V. L. Hartley proposed a logarithmic measure of information that illustrates this observation.

Type
Chapter
Information
Theory and Design of Digital Communication Systems , pp. 122 - 176
Publisher: Cambridge University Press
Print publication year: 2010

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

Shannon, C. E., “A mathematical theory of communication,”Bell Syst. Tech. J., Vol. 27, pp. 379–423, pp. 623–656, 1948.CrossRefGoogle Scholar
Shannon, C. E., “Communication in the presence of noise,”Proc. IRE, Vol. 37, pp. 10–21, 1949.CrossRefGoogle Scholar
Hartley, R. V. L., “The transmission of information,”Bell Syst. Tech. J., Vol. 7, pp. 535–563, 1928.CrossRefGoogle Scholar
Lin, S. and Costello, D. J., Jr., Error Control Coding, 2nd edition, Englewood Cliffs, NJ: Pearson Prentice-Hall, 2004.Google Scholar
Clark, G. C., Jr. and Cain, J. B., Error-Correction Coding for Digital Communications, New York: Plenum Press, 1981.CrossRefGoogle Scholar
Hamming, R. W., “Error detecting and error correcting codes,”Bell Syst. Tech. J., Vol. 29, pp. 147–160, 1950.CrossRefGoogle Scholar
Gallager, R., “Low-density parity-check codes,”IRE Trans. Inform. Theory, pp. 21–28, January 1962.CrossRefGoogle Scholar
Gallager, R., Low-Density Parity-Check Codes, Cambridge, MA: MIT Press, 1963.Google Scholar
Hamming, R. W., Coding and Information Theory, 2nd edition, London: Prentice-Hall, 1986.Google Scholar
Abramson, N., Information Theory and Coding, New York: McGraw-Hill, 1963.Google Scholar
Gallager, R. G., Information Theory and Reliable Communication, New York: Wiley, 1968.Google Scholar
Blahut, R. E., Principles and Practice of Information Theory, Reading, MA: Addison-Wesley, 1987.Google Scholar
Cover, T. M. and Thomas, J. A., Elements of Information Theory, 2nd edition, Chichester: John Wiley & Sons, 2006.Google Scholar
Barry, J. R., Lee, E. A., and Messerschmitt, D. G., Digital Communication, 3rd edition, Amsterdam: Kluwer Academic Publishers, 2004.CrossRefGoogle Scholar
Gallager, R. G., Principles of Digital Communications, Cambridge: Cambridge University Press, 2008.CrossRefGoogle Scholar
Lapidoth, A., A Foundation in Digital Communication, Cambridge: Cambridge University Press, 2009.CrossRefGoogle Scholar
MacKay, D., “Good error correcting codes based on very sparse matrix,”IEEE Trans. Inform. Theory, pp. 399–431, 1999.CrossRefGoogle Scholar
Richardson, T. J. and Urbanke, R., “Efficient encoding of low-density parity-check codes,”IEEE Trans. Inform. Theory, Vol. 47, No. 2, pp. 638–656, 2001.CrossRefGoogle Scholar
Shannon, C. E., “Communication theory of secrecy systems,”Bell Syst. Tech. J., Vol. 28, pp. 656–715, 1949.CrossRefGoogle Scholar
Shannon, C. E., “Prediction and entropy of printed English,”Bell Syst. Tech. J., Vol. 30, pp. 50–64, 1951.CrossRefGoogle Scholar
Shannon, C. E., “The zero error capacity of a noisy channel,”IRE Trans. Inform. Theory, Vol. IT-2, pp. 8–19, 1956.CrossRefGoogle Scholar
Shannon, C. E., “Certain results in coding theory for noisy channels,”Inform. Contr., Vol. 1, pp. 6–25, 1957.CrossRefGoogle Scholar
Shannon, C. E., “Channels with side information at the transmitter,”IBM J. Res. Develop., Vol. 2, pp. 289–293, 1958.CrossRefGoogle Scholar
Shannon, C. E., “Coding theorems for a discrete source with a fidelity criterion,”IRE Nat. Conv. Rec., Part 4, Vol. 2, pp. 142–143, 1959.Google Scholar
Shannon, C. E., “Probability of error for optimal codes in a Gaussian channel,”Bell Syst. Tech. J, Part 4, Vol. 38, pp. 611–656, 1959.CrossRefGoogle Scholar
Shannon, C. E., Gallager, R. G., and Berlekamp, E. R., “Lower bounds to error probability for coding on discrete memoryless channels, I and II,”Inform. Contr., Vol. 10, pp. 65–103, pp. 527–552, 1967.CrossRefGoogle Scholar
Tanner, R. M., “A recursive approach to low complexity codes,”IEEE Trans. Inform. Theory, Vol. IT-27, pp. 533–547, 1981.CrossRefGoogle Scholar
Wilson, S. G., Digital Modulation and Coding, Englewood Cliffs, NJ: Prentice-Hall, 1996.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org 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.

  • Information theory and channel coding
  • Tri T. Ha, Naval Postgraduate School, Monterey, California
  • Book: Theory and Design of Digital Communication Systems
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511778681.005
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.

  • Information theory and channel coding
  • Tri T. Ha, Naval Postgraduate School, Monterey, California
  • Book: Theory and Design of Digital Communication Systems
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511778681.005
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.

  • Information theory and channel coding
  • Tri T. Ha, Naval Postgraduate School, Monterey, California
  • Book: Theory and Design of Digital Communication Systems
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511778681.005
Available formats
×