Abstract
Generalized error-locating codes are discussed. An algorithm for calculation of the upper bound of the probability of erroneous decoding for known code parameters and the input error probability is given. Based on this algorithm, an algorithm for selection of the code parameters for a specified design and input and output error probabilities is constructed. The lower bound of the probability of erroneous decoding is given. Examples of the dependence of the probability of erroneous decoding on the input error probability are given and the behavior of the obtained curves is explained.
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References
F. R. Gantmacher, The Theory of Matrices (Nauka, Moscow, 1966; Chelsea, New York, 1959) [in Russian].
E. L. Blokh and V. V. Zyablov, Linear Concatenated Codes (Nauka, Moscow, 1982) [in Russian].
E. L. Blokh and V. V. Zyablov, Generalized Concatenated Codes (Svyaz’, Moscow, 1976) [in Russian].
V. V. Zyablov, New Interpretation of Error Location Codes, Their Correcting Properties, and Decoding Algorithms (Nauka, Moscow, 1972) [in Russian].
I. G. Kobozeva and V. V. Zyablov, “Using GEL codes for optical channel,” in Proc. 12th Int. Symp. on Problems of Redundancy in Information Systems, St. Petersburg, Russia, May 26–30, 2009 (St-Petersburg State Univ. of Aerospace Instrumentation, St. Petersburg, 2009), pp. 126–127.
A. O. Nekuchaev and V. V. Zyablov, “Project “Continent”: a new approach to data transmission over backbone fiber-optic communication lines,” FotonEkspress, No. 3, 40–42 (2008).
J. Maucher, V. Zyablov, and M. Bossert, “On the equivalence of generalized concatenated codes and generalized error location codes,” IEEE Trans. Inf. Theory 46, 642–649 (2000).
V. V. Zyablov and I. G. Kobozeva, “Code constructions on the basis of three-dimensional generalized error location codes,” Inf. Protsessy 13 (1), 1–18 (2013).
J. K. Wolf and B. Elspas, “Error location codes—a new concept in error control,” IEEE Trans. Inf. Theory 9, 113–117 (1965).
J. K. Wolf, “On an extended class of error location codes,” Inf. Control., 8, 163–169 (1965).
A. Fahrner, H. Griesser, R. Klarer, V. V. Zyablov, “Lowcomplexity GEL codes for digital magnetic storage systems,” IEEE Trans. Magn. 40, 3093–3095 (2004).
A. Fahrner, H. Griesser, R. Klarer, and V. V. Zyablov, “Generalized error location codes for digital magnetic storage systems,” in Proc. 5th Int. ITG 2004 Conf. Source Channel Coding (SCC), Erlangen, Germany, Jan. 14–16, 2004 (VDE Verlag, Berlin, 2004), pp. 219–226.
V. B. Afanas’ev and E. M. Gabidulin, Coding in Radio Electronics (Radio i svyaz', Moscow, 1986) [in Russian].
I. V. Zhilin, F. I. Ivanov, P. S. Rybin, and V. V. Zyablov, “GEL codes on the basis of binary LDPC codes,” in Information Technologies and Systems (Proc. 36th Int. Conf. Young Researchers and Specialists, Kaliningrad, 2013) (State Univ. Aerospace Instrument, St. Petersburg, 2013), pp. 485–489.
I. Zhilin and V. Zyablov, “LDPC Code construction as a generalized concatenated code,” in Proc. 2014 14th Int. Symp. “Problems of Redundancy in Information and Control Systems”, ISBN 978-5-8088-0909-3.
A. A. Kreshchuk and V. V. Zyablov, “Generalized cconcatenated system with embedded space-time codes for MIMO systems,” Inf. Protsessy 14 (2), 160–177 (2014).
A. A. Kreshchuk and V. V. Zyablov, “Generalized concatenated system with embedded space-time codes for MIMO systems”. J. Comm. Technol. Electron. 59, 1489–1500 (2014).
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Original Russian Text © I.V. Zhilin, A.A. Kreshchuk, V.V. Zyablov, 2014, published in Informatsionnye Protsessy, 2014, Vol. 14, No. 4, pp. 370–384.
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Zhilin, I.V., Kreshchuk, A.A. & Zyablov, V.V. Generalized error-locating codes and minimization of redundancy for specified input and output error probabilities. J. Commun. Technol. Electron. 60, 695–706 (2015). https://doi.org/10.1134/S1064226915060212
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DOI: https://doi.org/10.1134/S1064226915060212