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International Conference on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes

AAECC 1987: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes pp 202–215Cite as

On generalized minimum distance decoding

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 356))

Abstract

A numerical method to compute the performance probabilities of GMD decoders is proposed for binary antipodal signaling on the AWGN channel with coherent reception. Plots of the probability of decoding failure and of the bit error rate are presented for triple-error-correcting extended BCH codes of length 64 and 128.

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References

  1. M. Abramowitz-I.A. Stegun, Handbook of Mathematical Functions. New York: Dover Publ., 1970.

    Google Scholar 

  2. E.R. Berlekamp, Key Papers in the Development of Coding Theory. New York: IEEE Press, 1974.

    Google Scholar 

  3. R.E. Blahut, Theory and Practice of Error Control Codes. Reading, Mass.: Addison-Wesley, 1983.

    Google Scholar 

  4. A. Dür, "On the computation of the performance probabilities for block codes with a bounded-distance decoding rule", IEEE Trans. Inform. Theory, vol. IT-34, pp.70–78, Jan. 1988.

    Article  Google Scholar 

  5. G. Einarsson-C.E. Sundberg, "A note on soft decision decoding with successive erasures," IEEE Trans. Inform. Theory, vol. IT-22, pp.88–96, Jan. 1976.

    Article  Google Scholar 

  6. W. Feller, An Introduction to Probability Theory and Its Applications. Vol.II. New York: Wiley, 1971.

    Google Scholar 

  7. G.D. Forney, Jr., "Generalized minimum distance decoding," IEEE Trans. Inform. Theory, vol. IT-12, pp.125–131, Apr. 1966.

    Article  Google Scholar 

  8. G.D. Forney, Jr., Concatenated Codes. Cambridge, Mass.: M.I.T. Press, 1966.

    Google Scholar 

  9. W. Gautschi, "Algorithm 363 — Complex Error Function," Comm. ACM., vol. 12, p.635, 1969.

    Article  Google Scholar 

  10. W. Gautschi, "Efficient computation of the complex error function," SIAM J. Numer. Anal., vol. 7, no. 1, pp.187–198, March 1970.

    Article  Google Scholar 

  11. P. Henrici, Applied and Computational Complex Analysis. Vol.II. New York: Wiley, 1977.

    Google Scholar 

  12. T. Kasami, "Weight distributions of Bose-Chaudhuri-Hocquenghem codes," Proc. Conf. Combinatorial Mathematics and Its Applications, R.C. Bose and T.A. Dowling, eds., University of North Carolina Press, Chapel Hill, N.C., 1968.

    Google Scholar 

  13. F.J. MacWilliams-N.J.A. Sloane, The Theory of Error-Correcting Codes. New York: North Holland, 1977.

    Google Scholar 

  14. J.L. Massey, Lecture Notes, Course 4052. Inst. Circuit Theory and Telecommun. Theory, Tech. Univ. Denmark, Lyngby, Spring 1972.

    Google Scholar 

  15. R. Piessens-E. de Doncker-Kapenga-C.W. Überhuber-D.K. Kahaner, Quadpack. Berlin: Springer, 1983.

    Google Scholar 

  16. C.C.H. Yu-D.J. Costello, Jr., "Generalized minimum distance decoding algorithms for Q-ary output channels," IEEE Trans. Inform. Theory, vol. IT-26, pp.238–243, Mar. 1980.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Innsbruck, Techniker-Straße 25, A-6020, Innsbruck, Austria

    Arne Dür

Authors
  1. Arne Dür
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Editor information

Llorenç Huguet Alain Poli

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© 1989 Springer-Verlag Berlin Heidelberg

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Dür, A. (1989). On generalized minimum distance decoding. In: Huguet, L., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1987. Lecture Notes in Computer Science, vol 356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51082-6_78

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  • DOI: https://doi.org/10.1007/3-540-51082-6_78

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51082-6

  • Online ISBN: 978-3-540-46150-0

  • eBook Packages: Springer Book Archive

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