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


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.

Publication DOI:
Divisions: College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: Copyright of EDP Sciences
Uncontrolled Keywords: low density parity check,error correcting codes,Galois fields,statistical physics,thermodynamical transition point,practical decoding phase,Physics and Astronomy(all)
Publication ISSN: 1286-4854
Last Modified: 02 Jan 2024 08:05
Date Deposited: 03 Aug 2009 11:24
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://iopscien ... 5-5075/56/4/610 (Publisher URL)
PURE Output Type: Article
Published Date: 2001-11-15
Authors: Nakamura, Kazutaka
Kabashima, Yoshiyuki
Saad, David (ORCID Profile 0000-0001-9821-2623)



Version: Published Version

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