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Probl. Peredachi Inf., 1975, Volume 11, Issue 1, Pages 23–36 (Mi ppi1568)  

This article is cited in 20 scientific papers (total in 20 papers)

Information Theory

Estimation of the error-correction complexity for Gallager low-density codes

V. V. Zyablov, M. S. Pinsker

Abstract: It is shown that among the Gallager low-density binary codes there are codes with decoding for the correction of all errors up to multiplicity $\alpha n$ and with decoding complexity of order $n\log n$, where $n$ is the code length and $\alpha$ is a positive number.

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English version:
Problems of Information Transmission, 1975, 11:1, 18–28

Bibliographic databases:

UDC: 621.391.15
Received: 05.09.1973

Citation: V. V. Zyablov, M. S. Pinsker, “Estimation of the error-correction complexity for Gallager low-density codes”, Probl. Peredachi Inf., 11:1 (1975), 23–36; Problems Inform. Transmission, 11:1 (1975), 18–28

Citation in format AMSBIB
\by V.~V.~Zyablov, M.~S.~Pinsker
\paper Estimation of the error-correction complexity for Gallager low-density codes
\jour Probl. Peredachi Inf.
\yr 1975
\vol 11
\issue 1
\pages 23--36
\jour Problems Inform. Transmission
\yr 1975
\vol 11
\issue 1
\pages 18--28

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    This publication is cited in the following articles:
    1. K. Engdahl, K. Sh. Zigangirov, “To the Theory of Low-Density Convolutional Codes. I”, Problems Inform. Transmission, 35:4 (1999), 295–310  mathnet  mathscinet  zmath
    2. K. Sh. Zigangirov, M. Lentmaier, “Mathematical Analysis of an Iterative Decoding Algorithm for Low-Density Codes”, Problems Inform. Transmission, 36:4 (2000), 314–324  mathnet  mathscinet  zmath
    3. D. V. Trukhachev, M. Lentmaier, K. Sh. Zigangirov, “Some Results Concerning the Design and Decoding of Turbo-Codes”, Problems Inform. Transmission, 37:3 (2001), 190–205  mathnet  crossref  mathscinet  zmath
    4. Lentmaier, M, “An analysis of the block error probability performance of iterative decoding”, IEEE Transactions on Information Theory, 51:11 (2005), 3834  crossref  mathscinet  isi
    5. D. K. Zinangirov, K. Sh. Zigangirov, “Decoding of Low-Density Codes with Parity-Check Matrices Composed of Permutation Matrices, Used for Transmission over an Erasure Channel”, Problems Inform. Transmission, 42:2 (2006), 106–113  mathnet  crossref  mathscinet
    6. K. Sh. Zigangirov, A. E. Pusane, D. K. Zinangirov, D. J. Costello, “On the Error-Correcting Capability of LDPC Codes”, Problems Inform. Transmission, 44:3 (2008), 214–225  mathnet  crossref  mathscinet  zmath  isi
    7. V. V. Zyablov, R. Johannesson, M. Lončar, “Low-complexity error correction of Hamming-code-based LDPC codes”, Problems Inform. Transmission, 45:2 (2009), 95–109  mathnet  crossref  mathscinet  zmath  isi
    8. V. V. Zyablov, P. S. Rybin, “Erasure correction by low-density codes”, Problems Inform. Transmission, 45:3 (2009), 204–220  mathnet  crossref  mathscinet  zmath  isi
    9. A. Frolov, V. V. Zyablov, “Asymptotic estimation of the fraction of errors correctable by $q$-ary LDPC codes”, Problems Inform. Transmission, 46:2 (2010), 142–159  mathnet  crossref  mathscinet  isi
    10. Barg A., Mazumdar A., “On the Number of Errors Correctable with Codes on Graphs”, IEEE Trans Inform Theory, 57:2 (2011), 910–919  crossref  isi  elib
    11. Rybin P., Zyablov V., “Asymptotic estimation of error fraction corrected by binary LDPC code”, 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), 2011, 351–355  crossref  isi
    12. V. V. Zyablov, P. S. Rybin, “Analysis of the relation between properties of LDPC codes and the Tanner graph”, Problems Inform. Transmission, 48:4 (2012), 297–323  mathnet  crossref  isi
    13. Ivanov F.I., Zhilin I.V., Zyablov V.V., “Algoritm dekodirovaniya kodov s maloi plotnostyu proverok na chetnost s bolshim rasparallelivaniem”, Informatsionno-upravlyayuschie sistemy, 2012, no. 6, 53–59  elib
    14. Protopopov L.N., “Optimizatsiya signalno-kodovykh konstruktsii po kriteriyu energeticheskoi effektivnosti”, Elektrosvyaz, 4 (2013), 47–50  elib
    15. Rybin P., “on the Error-Correcting Capabilities of Low-Complexity Decoded Irregular Ldpc Codes”, 2014 IEEE International Symposium on Information Theory (Isit), IEEE International Symposium on Information Theory, IEEE, 2014, 3165–3169  isi
    16. P. S. Rybin, V. V. Zyablov, “Asymptotic bounds on the decoding error probability for two ensembles of LDPC codes”, Problems Inform. Transmission, 51:3 (2015), 205–216  mathnet  crossref  isi  elib
    17. I. V. Zhilin, F. I. Ivanov, “Vectorizing computations at decoding of nonbinary codes with small density of checks”, Autom. Remote Control, 77:10 (2016), 1781–1791  mathnet  crossref  isi  elib
    18. Frolov A. Zyablov V., “On the Multiple Threshold Decoding of Ldpc Codes Over Gf(Q)”, Adv. Math. Commun., 11:1 (2017), 123–137  crossref  isi
    19. Rybin P. Frolov A., “On the Decoding Radius Realized By Low-Complexity Decoded Non-Binary Irregular Ldpc Codes”, Proceedings of 2018 International Symposium on Information Theory and Its Applications (Isita2018), IEEE, 2018, 384–388  crossref  isi
    20. Rybin P. Frolov A., 2018 10Th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (Icumt 2018): Emerging Technologies For Connected Society, International Conference on Ultra Modern Telecommunications and Control Systems & Workshops, IEEE, 2018  isi
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