Statistical mechanics of low-density parity check error-correcting codes over Galois fields
Kazutaka Nakamura, 樺島 祥介, Yoshiyuki Kabashima +1 more
(received; accepted) PACS. 89.90+n – Other areas of general interest to physicists. PACS. 89.70+c – Information science. PACS. 05.50+q – Lattice theory and statistics; Ising problems. 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 nonzero 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-dependencies 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. Error correction mechanisms are essential for ensuring reliable data transmission through noisy media. They play an important role in a wide range of applications from magnetic hard
•Jan 1, 2001•14 citations