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On (Partial) unit memory codes based on Gabidulin codes

  • Coding Theory
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Abstract

(Partial) unit memory ((P)UM) codes provide a powerful possibility to construct convolutional codes based on block codes in order to achieve a high decoding performance. In this contribution, a construction based on Gabidulin codes is considered. This construction requires a modified rank metric, the so-called sum rank metric. For the sum rank metric, the free rank distance, extended row rank distance, and its slope are defined analogous to the extended row distance in the Hamming metric. Upper bounds for the free rank distance and slope of (P)UM codes in the sum rank metric are derived, and an explicit construction of (P)UM codes based on Gabidulin codes is given.

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Authors and Affiliations

  1. Institute of Telecommunications and Applied Information Theory (TAIT), Ulm University, Ulm, Germany

    A. Wachter & M. Bossert

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

    V. R. Sidorenko

  3. Ulm University, Ulm, Germany

    V. R. Sidorenko

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

    V. V. Zyablov

Authors
  1. A. Wachter
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  2. V. R. Sidorenko
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  3. M. Bossert
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  4. V. V. Zyablov
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Correspondence to A. Wachter.

Additional information

Original Russian Text © A. Wachter, V.R. Sidorenko, M. Bossert, V.V. Zyablov, 2011, published in Problemy Peredachi Informatsii, 2011, Vol. 47, No. 2, pp. 38–51.

Supported in part by the DFG, Grant no. Bo867/21-1.

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Wachter, A., Sidorenko, V.R., Bossert, M. et al. On (Partial) unit memory codes based on Gabidulin codes. Probl Inf Transm 47, 117–129 (2011). https://doi.org/10.1134/S0032946011020049

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  • DOI: https://doi.org/10.1134/S0032946011020049

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