Skip to main content

On the Capacity of Peak Power Constrained Gaussian Channels

  • Chapter
Performance Limits in Communication Theory and Practice

Part of the book series: NATO ASI Series ((NSSE,volume 142))

Abstract

The most interesting and important results on the performance of communication systems have been obtained when a peak power constraint has been imposed on the transmitted signals. While such a constraint afforded analytical tractability, in many cases, real-life systems are naturally limited in their peak excursion. This talk is devoted to the influence of a peak power limitation on the information rates of various models of practical communication systems.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Shannon CE: A mathematical theory of communication, (BSTJ, 379–423, 1948; A mathematical theory of communication, BSTJ, 623–656, October 1948; Communication in the presence of noise, Proc. IRE, Jan. 1949: all reprinted in: Key Papers in the Development of Information Theory, D. Slepian (ed.) pp 5–46, N.Y., N.Y. IEEE Press, 1974.

    Google Scholar 

  2. Smith JG: The information capacity of amplitude and variance-constrained scalar Gaussian channels, Inf. and Contr., vol. 18, pp 203–219, 1971.

    Article  MATH  Google Scholar 

  3. Smith JG: On the information capacity of peak and average power constrained Gaussian Channels, Ph.D. Dissertation, Dept. of Electrical Engineering, University of California, Berkeley, California.

    Google Scholar 

  4. Farber G: Die Kanalkapazitat Allgemeiner Ubertragunskanale Bei Begrenztem Signalwertbereich, Beliebigen Signalubertragungszeiten Sowie Beliebiger Sturung, Arch. Elektr. Ubertr. 21, H.11, S. 565–574, and H.12, S. 653–660, 1967.

    Google Scholar 

  5. McEliece RJ: The theory of information and coding, Encyclopedia of Mathematics and its Application, vol. 3, Addison-Wesley, 1977.

    Google Scholar 

  6. Gallager RG: Information theory and reliable communication, Wiley, New York, 1968.

    MATH  Google Scholar 

  7. Ozarow L, Wyner AD and Ziv J: Achievable rates for a constrained Gaussian channel, submitted for publication in IEEE Trans, on Information Theory, 1986.

    Google Scholar 

  8. Shitz S and Bar-David I: Peak power constraint and bandlimiting reduces capacity, EE Pub No. 593, Technion, Israel, June 1986.

    Google Scholar 

  9. McMillan B: A history of a problem, J. Soc. Indust. Appl. Math. vol. 3, 114–128, 1955.

    MathSciNet  Google Scholar 

  10. Wyner AD: Bounds on communication with polyphase coding, BSTJ, 523–559, April 1966.

    Google Scholar 

  11. Shitz S and Bar-David I: Capacity of peak and average-power limited-quadrature Gaussian channel, EE Pub No. 533, Technion, Israel, December 1985.

    Google Scholar 

  12. Forney Jr GD, Gallager RG, Lang GR, Longstaff FM and Qureshi SU: Efficient modulation for band-limited channels, IEEE J. SAC-2, No. 5, 632–647, September 1984.

    Google Scholar 

  13. Blachman NM: Capacities of amplitude- and phase-modulation, Proc. IRE, vol. 41, 748–759, June 1953.

    Article  Google Scholar 

  14. Ungerboeck G: Channel coding with multilevel/phase signals, IEEE Trans on IT, vol. IT-28, 55–67, January 1982.

    Article  Google Scholar 

  15. Saleh ARM and Salz J: On the computational cut-off rate, R, for the Peak-Power-Limited Gaussian Channel, Internal Report AT & T Bell Labs, Holmdel, New Jersey, submitted for publication in the IEEE Trans, on Communications.

    Google Scholar 

  16. Einarsson G: Signal design for the amplitude limited Gaussian channel by error bound optimization, IEEE Trans on Comm, vol. COM-27, No. 1, 152–158, January 1979.

    Article  Google Scholar 

  17. Shitz S and Bar-David I: Capacity bandwidth trade-off for a class of constant envelope modulations, EE Pub. No. 532, Technion, Israel, December 1985.

    Google Scholar 

  18. Masseng T: Digitally phase modulated (DPM) signals, IEEE Trans, on Comm. Vol. COM-33, No. 9, 911–918, September 1985.

    Article  Google Scholar 

  19. Slepian D: On Maxentropic discrete stationary processes, BSTJ, 629–653 March 1972.

    Google Scholar 

  20. Mcliece, RJ, Rotemich ER and Swanson L: An entropy maximization problem to optical communications, submitted for publication in the IEEE Trans, on Inf. Theory.

    Google Scholar 

  21. Bar-David I and Shitz S: Information transfer by random telegraph vs. phase modulation with relevance to magnetic recording, EE Pub. No. 568 Technion, Israel, January 1986.

    Google Scholar 

  22. Duncan TE: On the calculation of mutual information, SIAM J. Appl. Math. vol. 19, no. 1, 215–220, July 1970.

    Article  MathSciNet  MATH  Google Scholar 

  23. Wonham WM: Some applications of stochastic differential equations to optimal nonlinear filtering, J. SIAM. Contr. Ser. A, vol. 2, 347–369, 1965.

    MathSciNet  MATH  Google Scholar 

  24. Bobrovsky BZ and Zakai M: Asymptotic a Priori estimates for the error in nonlinear filtering problem, IEEE Trans, on Inf. Th., vol. IT-28, 371–376, March 1982.

    Article  MathSciNet  Google Scholar 

  25. Anderson JB, Aulin T and Sundberg C-E: Digital phase modulation, textbook to be published 1986.

    Google Scholar 

  26. Omura JK and Jackson D: Cut-off rates for channels using bandwidth efficient modulations, pp. 14.1.1–14.1.11, NTC-1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Kluwer Academic Publishers

About this chapter

Cite this chapter

Bar-David, I. (1988). On the Capacity of Peak Power Constrained Gaussian Channels. In: Skwirzynski, J.K. (eds) Performance Limits in Communication Theory and Practice. NATO ASI Series, vol 142. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2794-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-2794-0_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7757-6

  • Online ISBN: 978-94-009-2794-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics