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 Probl. Peredachi Inf., 2000, Volume 36, Issue 4, Pages 3–24 (Mi ppi490)

Information Theory

On the Relation between the Code Spectrum and the Decoding Error Probability

M. V. Burnashev

Abstract: We show how to lower bound the best decoding error probability (or upper bound the reliability function) given some estimates for the code spectrum. Bounds thus obtained are better than previously known ones.

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English version:
Problems of Information Transmission, 2000, 36:4, 285–304

Bibliographic databases:

UDC: 621.391.15

Citation: M. V. Burnashev, “On the Relation between the Code Spectrum and the Decoding Error Probability”, Probl. Peredachi Inf., 36:4 (2000), 3–24; Problems Inform. Transmission, 36:4 (2000), 285–304

Citation in format AMSBIB
\Bibitem{Bur00} \by M.~V.~Burnashev \paper On the Relation between the Code Spectrum and the Decoding Error Probability \jour Probl. Peredachi Inf. \yr 2000 \vol 36 \issue 4 \pages 3--24 \mathnet{http://mi.mathnet.ru/ppi490} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1813648} \zmath{https://zbmath.org/?q=an:0986.94050} \transl \jour Problems Inform. Transmission \yr 2000 \vol 36 \issue 4 \pages 285--304 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Barg A., McGregor A., “More on the reliability function of the BSC”, 2003 IEEE International Symposium on Information Theory - Proceedings, 2003, 115–115
2. Cohen, A, “Lower bounds on the error probability of block codes based on improvements on de Caen's inequality”, IEEE Transactions on Information Theory, 50:2 (2004), 290
3. Tillich, JP, “The Gaussian isoperimetric inequality and decoding error probabilities for the Gaussian channel”, IEEE Transactions on Information Theory, 50:2 (2004), 328
4. M. V. Burnashev, “Sharpening of the Upper Bound for the Reliability Function of a Binary Symmetric Channel”, Problems Inform. Transmission, 41:4 (2005), 301–318
5. Barg, A, “Distance distribution of binary codes and the error probability of decoding”, IEEE Transactions on Information Theory, 51:12 (2005), 4237
6. M. V. Burnashev, “Code Spectrum and the Reliability Function: Binary Symmetric Channel”, Problems Inform. Transmission, 42:4 (2006), 263–281
7. Ben-Haim Ya., Litsyn S., “Improved upper bounds on the reliability function of the Gaussian channel”, 2006 IEEE International Symposium on Information Theory, 2006, 709–713
8. M. V. Burnashev, “Code Spectrum and the Reliability Function: Gaussian Channel”, Problems Inform. Transmission, 43:2 (2007), 69–88
9. Burnashev M.V., “New results on the reliability function of the Gaussian channel”, 2007 IEEE International Symposium on Information Theory Proceedings, 2007, 471–474
10. Ben-Haim, Y, “Improved upper bounds on the reliability function of the Gaussian channel”, IEEE Transactions on Information Theory, 54:1 (2008), 5
11. M. V. Burnashev, “On the BSC reliability function: expanding the region where it is known exactly”, Problems Inform. Transmission, 51:4 (2015), 307–325
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