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Abstract

In the last decade two old methods for decoding linear block codes have gained considerable interest, iterative decoding as first described by Gallager in [1] and list decoding as introduced by Elias [2]. In particular iterative decoding of lowdensity parity-check (LDPC) codes, has been an important subject of research, see e.g. [3] and the references therein. “Good“ LDPC codes are often randomly generated by computer, but recently codes with an algebraic or geometric structure have also been considered e.g [3] and [4]. The performance of the iterative decoder is typically studied by simulations and a theoretical analysis is more difficult.

References

  1. 1.
    Gallager, R.G.: Low-Density Parity-Check Codes. M.I.T. Press, Cambridge, MA (1963)Google Scholar
  2. 2.
    Elias, P.: List Decoding for Noisy Channel. Res. Lab. Electron., MIT, Cambridge, MA, Techn. Rep. 335 (1957)Google Scholar
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    Kou, Y., Lin, S., Fossorier, M.: Low-Density Parity-Check Codes Based on Finite Geometries: A Rediscovery and New Results. IEEE Trans. Inform. Theory 47, 2711–2736 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
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    Liu, Z., Pados, D.A.: LDPC Codes from Generalized Polygons. IEEE Trans. Inform. Theory 51, 3890–3898 (2005)CrossRefMathSciNetGoogle Scholar
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    Bossert, M., Hergert, F.: Hard-and Soft-Decision Decoding Beyond the Half Minimum Distance - An Algorithm for Linear Codes. IEEE Trans. Inform. Theory 32, 709–714 (1986)zbMATHCrossRefGoogle Scholar
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    Hjaltason, J.: List Decoding of LDPC Codes. M. Eng. Thesis, Department of Mathematics, Technical University of Denmark (2005)Google Scholar
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    Justesen, J., Høholdt, T., Hjaltason, J.: Iterative List Decoding of Some LDPC Codes. IEEE Trans. Inform. Theory. (to appear, 2007)Google Scholar
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    Kristensen, J.T.: List Decoding of LDPC Codes. M. Eng. Thesis, COM, Technical University of Denmark (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Tom Høholdt
    • 1
  • Jørn Justesen
    • 2
  1. 1.Department of Mathematics, The Technical University of Denmark Bldg.303 DK-2800 LyngbyDenmark
  2. 2.COM, The technical University of Denmark Bldg 343 DK-2800 LyngbyDenmark

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