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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
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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.

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

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References

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  • 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
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  • 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
×