Statistical mechanics of low-density parity check error-correcting codes over Galois fields

Kazutaka Nakamura, Yoshiyuki Kabashima, David Saad

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A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF(q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different q-dependence in the cases of C = 2 and C ≥ 3; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

Original languageEnglish
Pages (from-to)610-616
Number of pages7
JournalEurophysics Letters
Issue number4
Publication statusPublished - 15 Nov 2001

Bibliographical note

Copyright of EDP Sciences


  • low density parity check
  • error correcting codes
  • Galois fields
  • statistical physics
  • thermodynamical transition point
  • practical decoding phase


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