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