Skip to main content

Vector Trellis Quantization for Noisy Channels

  • Chapter

Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 114))

Abstract

The channel coding theorem of information theory indicates that if the rate of a binary sequence is less than the capacity of the channel over which the binary sequence is to be transmitted, then the source can be reproduced at the channel output with arbitrarily small error probability [1], [2]. Based on this, one can isolate the problem of channel coding from that of source coding. In other words, channel encoder, channel, and channel decoder may be considered as a noiseless link between the output of the source encoder and the input of source decoder, as long as source encoder’s output has a rate less than the capacity of the channel [3]. However, this separation is optimal only asymptotically, i.e., in the limit of arbitrarily complex overall encoders and decoders involving arbitrarily long blocklengths. In practice, where we encounter the curse of complexity and are forced to deal with finite blocklengths, such a separation results in a certain degree of sub-optimality.

Research supported by Canada Natural Science and Engineering Council Grant OG PIN 011.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. CE. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423 and 623-656, 1948.

    MathSciNet  MATH  Google Scholar 

  2. R. G. Galleger, Information theory and reliable communication, John Wiley & Sons, N.Y. 1968.

    Google Scholar 

  3. A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding, McGraw Hill, N.Y. 1979.

    Google Scholar 

  4. N. Farvardin and V. Vaishampayan, “Optimal Quantizer Design for Noisy Channels: An Approach to Combined Source-Channel Coding,” IEEE Trans. Inform. Theory, pp. 827–888, Nov. 1987.

    Google Scholar 

  5. N. Farvardin and V. Vaishampayan, “Some Issues of Vector Quantizers for Noisy Channels,” IEEE Symp. on Information Theory, Kobe, Japan, June 19–24, 1988.

    Google Scholar 

  6. K. Zeger, and A. Gersho, “Theory and Design of Optimal Noisy Channel Vector Quantizers,” IEEE Trans. Inform. Theory.

    Google Scholar 

  7. E. Ayanoğlu and R. M. Gray, “The Design of Joint Source and Channel Trellis Waveform Coders,” IEEE Trans. Inform. Theory, vol. IT-33, pp. 855–865, Nov. 1987.

    Article  MathSciNet  Google Scholar 

  8. J. G. Dunham and R. G. Gray, “Joint Source and Noisy Channel Trellis Encoding,” IEEE Trans. Inform., vol. IT-27, pp. 516–519, July 1981.

    Article  MathSciNet  MATH  Google Scholar 

  9. B. H. Juang, “Design of Trellis Vector Quantizers for Speech Signals,” IEEE Trans. Acousitcs, Speech, and Signal Processing, Vol. 36, pp. 1423–1431, Sept. 1988.

    Article  MATH  Google Scholar 

  10. C. D. Bei and R. M. Gray, “Simulation of Vector Trellis Encoding Systems,” IEEE Trans. Commun., vol. COM-34, pp. 214–218, Mar. 1986.

    Google Scholar 

  11. G. D. Forney, JR. “The Viterbi Algorithm,” Proc. IEEE, vol. 61, pp. 268–178, Mar. 1973.

    Article  MathSciNet  Google Scholar 

  12. F. Jelinek and J. B. Anderson, “Instrumentable tree encoding of information sources,” IEEE Trans. Inform. Theory, vol. IT-17, pp. 118–119, Jan. 1971.

    Article  MATH  Google Scholar 

  13. Y. Linde, A. Buzo and R. M. Gray, “An Algorithm for Vector Quantizer Design,” IEEE Trans. Commun., vol. COM-28, pp. 84–95, Jan. 1980.

    Article  Google Scholar 

  14. L. C. Stewart, R. M. Gray and Y. Linde “The Design of Trellis Waveform Coders,” IEEE Trans. Commun. vol. COM-30, pp. 702–710, April 1982.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Soleymani, M.R., Khandani, A.K. (1991). Vector Trellis Quantization for Noisy Channels. In: Atal, B.S., Cuperman, V., Gersho, A. (eds) Advances in Speech Coding. The Springer International Series in Engineering and Computer Science, vol 114. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3266-8_26

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-3266-8_26

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6437-5

  • Online ISBN: 978-1-4615-3266-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics