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Decoding a Perturbed Sequence Generated by an LFSR

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Coding Theory and Applications (ICMCTA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10495))

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Abstract

Given a sequence of bits produced by a linear feedback shift register (LFSR), the Berlekamp-Massey algorithm finds a register of minimal length able to generate the sequence. The situation is different when the sequence is perturbed; for instance, when it is sent through a transmission channel. LFSRs can be described as autonomous systems. A perturbed sequence of bits generated by an LFSR can be interpreted as a codeword in the binary linear code generated by the corresponding observability matrix. The problem of finding the original sequence can then be stated as the decoding problem, “given the received codeword, find the information transmitted”. We propose two decoding algorithms, one based on a brute force attack and the other one based on the representation technique of the syndromes introduced by Becker, Joux, May, and Meurer (2012).

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Acknowledgements

The first author was supported by FAPESP with number of process 2015/07246-0. The second author was partially supported by grants MIMECO MTM2015-68805-REDT and MTM2015-69138-REDT. The third author was partially supported by grants MINECO MTM2013-40960-P and MTM2015-68805-REDT.

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Authors and Affiliations

  1. Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas (UNICAMP), R. Sérgio Buarque de Holanda, 651, Cidade Universitária, Campinas, SP, 13083-859, Brazil

    Sara D. Cardell

  2. Departament de Matemàtiques, Universitat d’Alacant, Ap. Correus 99, 03080, Alacant, Spain

    Joan-Josep Climent

  3. Departamento de Matemática Aplicada, IMM, Universitat Politècnica de València, Camí de Vera, s/n, 46022, València, Spain

    Alicia Roca

Authors
  1. Sara D. Cardell
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  2. Joan-Josep Climent
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  3. Alicia Roca
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Corresponding author

Correspondence to Joan-Josep Climent .

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Editors and Affiliations

  1. University of Valladolid, Valladolid, Spain

    Ángela I. Barbero

  2. University of Tartu, Tartu, Estonia

    Vitaly Skachek

  3. Simula@UiB and University of Bergen, Bergen, Norway

    Øyvind Ytrehus

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Cardell, S.D., Climent, JJ., Roca, A. (2017). Decoding a Perturbed Sequence Generated by an LFSR. In: Barbero, Á., Skachek, V., Ytrehus, Ø. (eds) Coding Theory and Applications. ICMCTA 2017. Lecture Notes in Computer Science(), vol 10495. Springer, Cham. https://doi.org/10.1007/978-3-319-66278-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-66278-7_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66277-0

  • Online ISBN: 978-3-319-66278-7

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