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Sharpening of an Upper Bound for the Reliability Function of a Binary Symmetric Channel

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Abstract

An upper bound for the reliability function of a binary symmetric channel is improved.

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REFERENCES

  1. Elias, P., Coding for Noisy Channels, IRE Conv. Rec., 1955, vol. 4, pp. 37–46. Reprinted in Key Papers in the Development of Information Theory, Slepian, D., Ed., New York: IEEE Press, 1974, pp. 102–111.

    Google Scholar 

  2. Shannon, C.E., Gallager, R.G., and Berlekamp, E.R., Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. I, II, Inform. Control, 1967, vol. 10, no.1, pp. 65–103; no. 5, pp. 522–552.

    Article  MathSciNet  Google Scholar 

  3. Gallager, R.G., A Simple Derivation of the Coding Theorem and Some Applications, IEEE Trans. Inform. Theory, 1965, vol. 11, no.1, pp. 3–18.

    Article  MATH  MathSciNet  Google Scholar 

  4. McEliece, R.J., Rodemich, E.R., Rumsey, H., Jr., and Welch, L.R., New Upper Bounds on the Rate of a Code via the Delsarte-MacWilliams Inequalities, IEEE Trans. Inform. Theory, 1977, vol. 23, no.2, pp. 157–166.

    Article  MathSciNet  Google Scholar 

  5. McEliece, R.J. and Omura, J.K., An Improved Upper Bound on the Block Coding Error Exponent for Binary-Input Discrete Memoryless Channels, IEEE Trans. Inform. Theory, 1977, vol. 23, no.5, pp. 611–613.

    Article  MathSciNet  Google Scholar 

  6. Litsyn, S., New Bounds on Error Exponents, IEEE Trans. Inform. Theory, 1999, vol. 45, no.2, pp. 385–398.

    Article  MATH  MathSciNet  Google Scholar 

  7. Burnashev, M.V., Limits of Attainable Accuracy for Transmission of a Parameter over a White Gaussian Channel, Probl. Peredachi Inf., 1977, vol. 13, no.4, pp. 9–24 [Probl. Inf. Trans. (Engl. Transl.), 1977, vol. 13, no. 4, pp. 251–260].

    MATH  MathSciNet  Google Scholar 

  8. Burnashev, M.V., A New Lower Bound for the α-Mean Error of Parameter Transmission over the White Gaussian Channel, IEEE Trans. Inform. Theory, 1984, vol. 30, no.1, pp. 23–34.

    Article  MATH  MathSciNet  Google Scholar 

  9. Burnashev, M.V., On Minimum Attainable Mean-Square Error in Transmission of a Parameter over a Channel with White Gaussian Noise, Probl. Peredachi Inf., 1985, vol. 21, no.4, pp. 3–16 [Probl. Inf. Trans. (Engl. Transl.), 1985, vol. 21, no. 4, pp. 247–257].

    MATH  MathSciNet  Google Scholar 

  10. Ashikhmin, A., Barg, A., and Litsyn, S., A New Upper Bound on the Reliability Function of the Gaussian Channel, IEEE Trans. Inform. Theory, 2000, vol. 46, no.6, pp. 1945–1961.

    Article  MathSciNet  Google Scholar 

  11. Burnashev, M.V., On the Relation between the Code Spectrum and the Decoding Error Probability, Probl. Peredachi Inf., 2000, vol. 36, no.4, pp. 3–24 [Probl. Inf. Trans. (Engl. Transl.), 2000, vol. 36, no. 4, pp. 285–304].

    MATH  MathSciNet  Google Scholar 

  12. Barg, A. and McGregor, A., Distance Distribution of Binary Codes and the Error Probability of Decoding, in Proc. Int. Workshop on Coding and Cryptography, Versailles, France, 2003, pp. 51–61.

  13. Barg, A. and McGregor, A., Distance Distribution of Binary Codes and the Error Probability of Decoding, submitted for publication in IEEE Trans. Inform. Theory.

  14. Kounias, E.G., Bounds on the Probability of a Union, with Application, Ann. Math. Statist., 1968, vol. 39, no.6, pp. 2154–2158.

    MATH  MathSciNet  Google Scholar 

  15. de Caen, D., A Lower Bound on the Probability of a Union, Discr. Math., 1997, vol. 169, pp. 217–220.

    MATH  Google Scholar 

  16. Cohen, A. and Merhav, N., Lower Bounds on the Error Probability of Block Codes Based on Improvements on de Caen's Inequality, IEEE Trans. Inform. Theory, 2004, vol. 50, no.2, pp. 290–310.

    Article  MathSciNet  Google Scholar 

  17. Levenstein, V.I., On the Straight-Line Bound for the Undetected Error Exponent, Probl. Peredachi Inf., 1989, vol. 25, no.1, pp. 33–37 [Probl. Inf. Trans. (Engl. Transl.), 1989, vol. 25, no. 1, pp. 24–27].

    Google Scholar 

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__________

Translated from Problemy Peredachi Informatsii, No. 4, 2005, pp. 3–22.

Original Russian Text Copyright © 2005 by Burnashev.

Supported in part by the Russian Foundation for Basic Research, project no. 03-01-00098, and INTAS, grant no. 00-738.

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Burnashev, M.V. Sharpening of an Upper Bound for the Reliability Function of a Binary Symmetric Channel. Probl Inf Transm 41, 301–318 (2005). https://doi.org/10.1007/s11122-006-0001-6

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  • DOI: https://doi.org/10.1007/s11122-006-0001-6

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