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Information--bit error rate and false positives in an MDS code

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  • In this paper, a computation of the input-redundancy weight enumerator is presented. This is used to improve the theoretical approximation of the information--bit error rate, in terms of the channel bit--error rate, in a block transmission through a discrete memoryless channel. Since a bounded distance reproducing encoder is assumed, we introduce the here-called false positive, a decoding failure with no information-symbol error, and we estimate the probability that this event occurs. As a consequence, a new performance analysis of an MDS code is proposed.
    Mathematics Subject Classification: Primary: 94B70, 94B05.


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  • [1]

    C. Desset, B. Macq and L. Vandendorpe, Computing the word-, symbol-, and bit-error rates for block error-correcting codes, IEEE Trans. Commun., 52 (2004), 910-921.doi: 10.1109/TCOMM.2004.829509.


    R. Dodunekova and S. M. Dodunekov, Sufficient conditions for good and proper error-detecting codes, IEEE Trans. Inf. Theory, 43 (1997), 2023-2026.doi: 10.1109/18.641570.


    R. Dodunekova and S. M. Dodunekov, The MMD codes are proper for error detection, IEEE Trans. Inf. Theory, 48 (2002), 3109-3111.doi: 10.1109/TIT.2002.805082.


    R. Dodunekova, S. M. Dodunekov and E. Nikolova, A survey on proper codes, Discrete Appl. Math., 156 (2008), 1499-1509.doi: 10.1016/j.dam.2005.06.014.


    M. El-Khamy, New Approaches to the Analysis and Design of Reed-Solomon Related Codes, Ph.D thesis, California Institute of Technology, 2007.


    M. El-Khamy and R. J. McEliece, Bounds on the average binary minimum distance and the maximum likelihood performance of Reed Solomon codes, in 42nd Allerton Conf. Commun. Control Comput., 2004.


    M. El-Khamy and R. J. McEliece, The partition weight enumerator of MDS codes and its applications, in Int. Symp. Inf. Theory, 2005, 926-930.doi: 10.1109/ISIT.2005.1523473.


    A. Faldum, J. Lafuente, G. Ochoa and W. Willems, Error probabilities for bounded distance decoding, Des. Codes Crypt., 40 (2006), 237-252.doi: 10.1007/s10623-006-0010-x.


    M. P. C. Fossorier, Critical point for maximum likelihood decoding of linear block codes, IEEE Commun. Letters, 9 (2005), 817-819.doi: 10.1109/LCOMM.2005.1506713.


    J. Han, P. H. Siegel and P. Lee, On the probability of undetected error for overextended Reed-Solomon codes, IEEE Trans. Inf. Theory, 52 (2006), 3662-3669.doi: 10.1109/ITW.2006.1633800.


    T. Kasami and S. Lin, On the probability of undetected error for the maximum distance separable codes, IEEE Trans. Commun., COM-32 (1984), 998-1006.doi: 10.1109/TCOM.1984.1096175.


    J. MacWilliams, A theorem on the distribution of weights in a systematic code, Bell System Tech. J., 42 (1963), 79-94.doi: 10.1002/j.1538-7305.1963.tb04003.x.


    F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes, North Holland Publishing Co., 1977.


    J. Riordan, Combinatorial Identities, Robert E. Krieger Publishing Co., Huntington, New York, 1979.


    S. Roman, Coding and Information Theory, Springer-Verlag, New York, 1992.


    W. A. Stein et al., Sage Mathematics Software (Version 5.9), The Sage Development Team, 2012, available at http://www.sagemath.org


    D. Torrieri, The information-bit error rate for block codes, IEEE Trans. Commun., COM-32 (1984), 474-476.doi: 10.1109/TCOM.1984.1096082.


    D. Torrieri, Information-bit, information-symbol, and decoded-symbol error rates for linear block codes, IEEE Trans. Commun., 36 (1988), 613-617.doi: 10.1109/26.1477.


    J. H. van Lint and R. M. Wilson, A Course in Combinatorics, 2nd edition, Cambridge University Press, 2001.doi: 10.1017/CBO9780511987045.


    K.-P. Yar, D.-S. Yoo and W. Stark, Performance of RS coded $M$-ary modulation with and without symbol overlapping, IEEE Trans. Commun., 56 (2008), 445-453.doi: 10.1109/TCOMM.2008.050229.

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