Skip to main content
Log in

Extension of some results for channel capacity using a generalized information measure

  • Published:
Applied Mathematics and Optimization Aims and scope Submit manuscript

Abstract

A new formulation for the channel capacity problem is derived by using the duality theory of convex programming. The simple nature of this dual representation is suitable for computational purposes. The results are derived in a unified way by formulating the channel capacity problem as a special case of a general class of concave programming problems involving a generalized information measure recently introduced by Burbea and Rao [10].

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aczel J (1984) Measuring information beyond communication theory—why some generalized information measures may be useful, others not. Aequationes Math 27:1–19.

    Google Scholar 

  2. Arimoto S (1972) An algorithm for computing the capacity of arbitrary discrete memoryless channels. IEEE Trans. Inform Theory 18:14–20

    Google Scholar 

  3. Arimoto S (1977) Information measures and capacity of orderα for discrete memoryless channels. In: Csiszar I, Elias P (eds) Topics in Information Theory. North-Holland, Amsterdam, pp 41–52

    Google Scholar 

  4. Armstrong RD, Godfrey JR (1979) Two linear programming algorithms for the discretel 1 norm problem. Math Comp 33:289–300

    Google Scholar 

  5. Barrodale I, Roberts FDK (1973) An improved algorithm for discretel 1 -linear approximation. SIAM J Numer Anal 10:839–848

    Google Scholar 

  6. Ben-Tal A, Teboulle M (1986) Rate distortion theory with generalized information measures via convex programming duality. IEEE Trans Inform Theory 32:630–641

    Google Scholar 

  7. Blahut RE (1972) Computation of channel capacity and rate distortion functions. IEEE Trans Inform Theory 28:489–495

    Google Scholar 

  8. Burbea J (1983)J-Divergence and related topics. Encyclopedia of Statistical Science vol. 4. Wiley, New York, pp 290–296

    Google Scholar 

  9. Burbea J (1984) The Bose-Einstein entropy of degreeα and its Jensen difference. Utilitas Math 25:225–240

    Google Scholar 

  10. Burbea J, Rao CR (1982) On the convexity of some divergence measures based on entropy functions. IEEE Trans Inform Theory 28:489–495

    Google Scholar 

  11. Burbea J, Rao CR (1982) Entropy differential metric, distance and divergence measures in probability spaces—a unified approach. J Multivariate Anal 12:575–596

    Google Scholar 

  12. Cheng MC (1979) On the computation of capacity of a discrete memoryless channel. Inform and Control 24:292–298

    Google Scholar 

  13. Csiszar I (1967) Information-type measures of difference of probability distributions and indirect observations. Studia Sci Math Hungar 2:299–318

    Google Scholar 

  14. Csiszar I, Korner J (1981) Information Theory: Coding Theorems for Discrete Memoryless systems. Academic Press, New York

    Google Scholar 

  15. Gallager RG (1968) Information Theory and Reliable Communication. Wiley, New York

    Google Scholar 

  16. Jelinek F (1968) Probabilistic Information Theory. McGraw-Hill, New York

    Google Scholar 

  17. Kiwiel KC (1985) Methods of Descent for Nondifferentiable Optimization. Lecture Notes in Mathematics, Vol 1133. Springer-Verlag, Berlin.

    Google Scholar 

  18. Lemarechal C (1975) An extension of Davidon methods to nondifferentiable problems. Math. Programming Stud 3:95–109

    Google Scholar 

  19. Lemarechal C (1980) Nondifferentiable optimization. In: Dixon, Spedicato, Szego (eds) Nonlinear Optimization Theory and Algorithms. Birkhauser, Boston

    Google Scholar 

  20. Meister B, Oettli W (1967) On the capacity of a discrete constant channel. Inform and Control 11:341–351

    Google Scholar 

  21. Muroga S (1953) On the capacity of a discrete channel. J. Phys Soc Japan 8:484–494

    Google Scholar 

  22. Rao CR, Nayak TK (1985) Cross entropy, dissimilarity measures, and characterizations of quadratic entropy. IEEE Trans Inform Theory 31:589–593

    Google Scholar 

  23. Renyi A (1961) On measures of entropy and information. Berkeley Symposium on Mathematical Statistics and Probability, vol. 1. University of California Press, Berkeley, pp 547–561

    Google Scholar 

  24. Rockafellar RT (1970) Convex Analysis. Princeton University Press, Princeton, NJ

    Google Scholar 

  25. Rockafellar RT (1974) Conjugate Duality and Optimization. Regional Conference Series in Applied Mathematics, no 16. SIAM, Philadelphia

    Google Scholar 

  26. Schittowsky K (1980) Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems, vol. 183. Springer-Verlag, Berlin

    Google Scholar 

  27. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423 and 623–565

    Google Scholar 

  28. Takano S (1975) On a method of calculating the capacity of a discrete memoryless channel. Inform and Control 29:327–336

    Google Scholar 

  29. Wolfe P (1975) A method of conjugate subgradients for minimizing nondifferentiable convex functions functions. Math. Programming Stud 3:145–173

    Google Scholar 

  30. Ziv J, Zakai M (1973) On functionals satisfying a data-processing theorem. IEEE Trans Inform Theory 19:275–283

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by M. Zakai

Research supported by National Science Foundation Grant No. ECS-8604354.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ben-Tal, A., Teboulle, M. Extension of some results for channel capacity using a generalized information measure. Appl Math Optim 17, 121–132 (1988). https://doi.org/10.1007/BF01448363

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01448363

Keywords

Navigation