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Probl. Peredachi Inf., 2015, Volume 51, Issue 2, Pages 50–56 (Mi ppi2169)  

This article is cited in 4 scientific papers (total in 4 papers)

Coding Theory

On error correction with errors in both the channel and syndrome

S. G. Vlăduţ, G. A. Kabatiansky, V. V. Lomakov

Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Abstract: We address the problem of error correction by linear block codes under the assumption that the syndrome of a received vector is found with errors. We propose a construction of parity-check matrices which allow to solve the syndrome equation even with an erroneous syndrome, in particular, parity-check matrices with minimum redundancy, which are analogs of Reed-Solomon codes for this problem. We also establish analogs of classical coding theory bounds, namely the Hamming, Singleton, and Gilbert–Varshamov bounds. We show that the new problem can be considered as a generalization of the well-known Ulam's problem on searching with a lie and as a discrete analog of the compressed sensing problem.

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English version:
Problems of Information Transmission, 2015, 51:2, 132–138

Bibliographic databases:

UDC: 621.391.15
Received: 12.01.2015
Revised: 17.02.2015

Citation: S. G. Vlăduţ, G. A. Kabatiansky, V. V. Lomakov, “On error correction with errors in both the channel and syndrome”, Probl. Peredachi Inf., 51:2 (2015), 50–56; Problems Inform. Transmission, 51:2 (2015), 132–138

Citation in format AMSBIB
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\paper On error correction with errors in both the channel and syndrome
\jour Probl. Peredachi Inf.
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\vol 51
\issue 2
\pages 50--56
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\transl
\jour Problems Inform. Transmission
\yr 2015
\vol 51
\issue 2
\pages 132--138
\crossref{https://doi.org/10.1134/S0032946015020040}
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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. V. S. Lebedev, “Coding with noiseless feedback”, Problems Inform. Transmission, 52:2 (2016), 103–113  mathnet  crossref  mathscinet  isi  elib  elib
    2. L. I. Rubanov, A. V. Seliverstov, “Projective-Invariant Description of a Meandering River”, J. Commun. Technol. Electron., 62:6 (2017), 663–668  crossref  isi  scopus
    3. V. Gritsenko, G. Kabatiansky, V. Lebedev, A. Maevskiy, “Signature Codes For Noisy Multiple Access Adder Channel”, Designs Codes Cryptogr., 82:1-2, SI (2017), 293–299  crossref  mathscinet  zmath  isi  scopus
    4. E. E. Egorova, V. S. Potapova, “Compositional restricted multiple access channel”, Problems Inform. Transmission, 54:2 (2018), 116–123  mathnet  crossref  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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