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Probl. Peredachi Inf., 2005, Volume 41, Issue 1, Pages 39–52 (Mi ppi87)  

This article is cited in 12 scientific papers (total in 12 papers)

Coding Theory

On the Minimum Distance of Low-Density Parity-Check Codes with Parity-Check Matrices Constructed from Permutation Matrices

A. Sridharana, M. Lentmaierb, D. V. Trukhachevc, D. J. Costelloa, K. Sh. Zigangirovda

a University of Notre Dame
b Institute of Communications and Navigation, German Aerospace Center
c University of Alberta
d Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: An ensemble of codes defined by parity-check matrices composed of $M\times M$ permutation matrices is considered. This ensemble is a subensemble of the ensemble of low-density parity-check (LDPC) codes considered by Gallager [1]. We prove that, as $M\to\infty$, the minimum distance of almost all codes in the ensemble grows linearly with $M$. We also show that in several cases the asymptotic minimum-distance-to-block-length ratio for almost all codes in the ensemble satisfies Gallager's bound [1].

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English version:
Problems of Information Transmission, 2005, 41:1, 33–44

Bibliographic databases:

UDC: 621.391.15:519
Received: 20.07.2004
Revised: 28.10.2004

Citation: A. Sridharan, M. Lentmaier, D. V. Trukhachev, D. J. Costello, K. Sh. Zigangirov, “On the Minimum Distance of Low-Density Parity-Check Codes with Parity-Check Matrices Constructed from Permutation Matrices”, Probl. Peredachi Inf., 41:1 (2005), 39–52; Problems Inform. Transmission, 41:1 (2005), 33–44

Citation in format AMSBIB
\Bibitem{SriLenTru05}
\by A.~Sridharan, M.~Lentmaier, D.~V.~Trukhachev, D.~J.~Costello, K.~Sh.~Zigangirov
\paper On~the Minimum Distance of Low-Density Parity-Check Codes with Parity-Check Matrices
Constructed from Permutation Matrices
\jour Probl. Peredachi Inf.
\yr 2005
\vol 41
\issue 1
\pages 39--52
\mathnet{http://mi.mathnet.ru/ppi87}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2125923}
\zmath{https://zbmath.org/?q=an:1078.94038}
\transl
\jour Problems Inform. Transmission
\yr 2005
\vol 41
\issue 1
\pages 33--44
\crossref{https://doi.org/10.1007/s11122-005-0008-4}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. Zigangirov D.K., Zigangirov K.Sh., “On the erasure correction capability of LDPC codes”, 2006 IEEE International Symposium on Information Theory, 2006, 416–420  crossref  isi
    3. Sridharan A., Truhachev D., Lentmaier M., Costello D.J. (Jr.), Zigangirov K.Sh., “Distance bounds for an ensemble of LDPC convolutional codes”, IEEE Trans. Inform. Theory, 53:12 (2007), 4537–4555  crossref  mathscinet  zmath  isi  elib
    4. 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
    5. Wang Chung-Li, Fossorier M., “On asymptotic ensemble weight enumerators of LDPC-like codes”, IEEE Journal on Selected Areas in Communications, 27:6 (2009), 899–907  crossref  isi
    6. Wang Ch.-L., Lin Sh., Fossorier M., “On Asymptotic Ensemble Weight Enumerators of Multi-Edge Type Codes”, Globecom 2009 - 2009 IEEE Global Telecommunications Conference, IEEE Global Telecommunications Conference (Globecom), 2009, 1289–1294  adsnasa  isi
    7. Lentmaier M., Fettweis G.P., Zigangirov K.Sh., Costello Daniel J. Jr., “Approaching Capacity with Asymptotically Regular LDPC Codes”, 2009 Information Theory and Applications Workshop, 2009, 170–174  isi
    8. Lentmaier M., Sridharan A., Costello Daniel J. Jr., Zigangirov K.Sh., “Iterative Decoding Threshold Analysis for LDPC Convolutional Codes”, IEEE Trans. Inform. Theory, 56:10 (2010), 5274–5289  crossref  zmath  isi  elib
    9. Truhachev D., Zigangirov K.Sh., Costello Daniel J. Jr., “Distance Bounds for Periodically Time-Varying and Tail-Biting LDPC Convolutional Codes”, IEEE Trans. Inform. Theory, 56:9 (2010), 4301–4308  crossref  mathscinet  isi  elib
    10. Zigangirov D.K., Zigangirov K.Sh., Costello Daniel J. Jr., “Partially-Regular LDPC Codes with Linear Encoding Complexity and Improved Thresholds”, 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), 2011, 528–532  crossref  isi
    11. 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
    12. 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
  • Проблемы передачи информации Problems of Information Transmission
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