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2 - Book overview

Published online by Cambridge University Press:  05 June 2012

William A. Pearlman  and
Amir Said
William A. Pearlman
Affiliation:
Rensselaer Polytechnic Institute, New York
Amir Said
Affiliation:
Hewlett-Packard Laboratories, Palo Alto, California
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Summary

Entropy and lossless coding

Compression of a digital signal source is just its representation with fewer information bits than its original representation. We are excluding from compression cases when the source is trivially over-represented, such as an image with gray levels 0 to 255 written with 16 bits each when 8 bits are sufficient. The mathematical foundation of the discipline of signal compression, or what is more formally called source coding, began with the seminal paper of Claude Shannon [1, 2], entitled “A mathematical theory of communication,” that established what is now called Information Theory. This theory sets the ultimate limits on achievable compression performance. Compression is theoretically and practically realizable even when the reconstruction of the source from the compressed representation is identical to the original. We call this kind of compression lossless coding. When the reconstruction is not identical to the source, we call it lossy coding. Shannon also introduced the discipline of Rate-distortion Theory [1–3], where he derived the fundamental limits in performance of lossy coding and proved that they were achievable. Lossy coding results in loss of information and hence distortion, but this distortion can be made tolerable for the given application and the loss is often necessary and unavoidable in order to satisfy transmission bandwidth and storage constraints. The payoff is that the degree of compression is often far greater than that achievable by lossless coding.

Type
Chapter
Information
Digital Signal Compression
Principles and Practice
 , pp. 10 - 22
Publisher: Cambridge University Press
Print publication year: 2011

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References

1. Shannon, C. E., “A mathematical theory of communication,” Bell Syst. Technol. J., vol. 27, pp. 379–423 and 632–656, July and Oct. 1948.CrossRefGoogle Scholar
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3. Shannon, C. E., “Coding theorems of a discrete source with a fidelity criterion,” in Information and Decision Processes, ed. Machol, R. E.New York, NY: McGraw-Hill Publishing Co., 1960, pp. 93–126.Google Scholar
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Pearlman, W. A., Islam, A., Nagaraj, N., and Said, A., “Efficient, low-complexity image coding with a set-partitioning embedded block coder,” IEEE Trans. Circuits Syst. Video Technol., vol. 14, no. 11, pp. 1219–1235, Nov. 2004.CrossRefGoogle Scholar
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Said, A. and Pearlman, W. A., “A new, fast, and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Syst. Video Technol., vol. 6, no. 3, pp. 243–250, June 1996.CrossRefGoogle Scholar
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  • Book overview
  • William A. Pearlman, Rensselaer Polytechnic Institute, New York, Amir Said, Hewlett-Packard Laboratories, Palo Alto, California
  • Book: Digital Signal Compression
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511984655.003
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  • Book overview
  • William A. Pearlman, Rensselaer Polytechnic Institute, New York, Amir Said, Hewlett-Packard Laboratories, Palo Alto, California
  • Book: Digital Signal Compression
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511984655.003
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.

  • Book overview
  • William A. Pearlman, Rensselaer Polytechnic Institute, New York, Amir Said, Hewlett-Packard Laboratories, Palo Alto, California
  • Book: Digital Signal Compression
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511984655.003
Available formats
×