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

Nakamura, Kazutaka, Kabashima, Yoshiyuki and Saad, David (2001). Statistical mechanics of low-density parity check error-correcting codes over Galois fields. Europhysics Letters, 56 (4), pp. 610-616.

Abstract

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: https://doi.org/10.1209/epl/i2001-00564-y
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied 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)
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://iopscien ... 5-5075/56/4/610 (Publisher URL)
Published Date: 2001-11-15
Authors: Nakamura, Kazutaka
Kabashima, Yoshiyuki
Saad, David ( 0000-0001-9821-2623)

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