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

Kazutaka Nakamura, Yoshiyuki Kabashima, David Saad

    Research output: Contribution to journalArticlepeer-review


    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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