Issue |
Europhys. Lett.
Volume 56, Number 4, November 2001
|
|
---|---|---|
Page(s) | 610 - 616 | |
Section | Interdisciplinary physics and related areas of science and technology | |
DOI | https://doi.org/10.1209/epl/i2001-00564-y | |
Published online | 01 December 2003 |
Statistical mechanics of low-density parity check error-correcting codes over Galois fields
1
Department of Computational Intelligence and Systems Science
Tokyo Institute of Technology - Yokohama 2268502, Japan
2
The Neural Computing Research Group, Aston
University - Birmingham B4 7ET, UK
Corresponding authors: knakamur@fe.dis.titech.ac.jp kaba@dis.titech.ac.jp saadd@aston.ac.uk
Received:
10
October
2000
Accepted:
22
August
2001
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 ; the analytical
solutions are in agreement with simulation results, providing a
quantitative measure to the improvement in performance obtained using
non-binary alphabets.
PACS: 89.90.+n – Other topics in areas of applied and interdisciplinary physics / 89.70.+c – Information science / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EDP Sciences, 2001
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