Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2001-06-17
Physics
Condensed Matter
Disordered Systems and Neural Networks
7 pages
Scientific paper
10.1103/PhysRevE.66.036125
The performance of ``typical set (pairs) decoding'' for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding, error happens when the information transmission is corrupted by an untypical noise or two or more typical sequences satisfy the parity check equation provided by the received codeword for which a typical noise is added. We show that the average error rate for the latter case over a given code ensemble can be tightly evaluated using the replica method, including the sensitivity to the message length. Our approach generally improves the existing analysis known in information theory community, which was reintroduced by MacKay (1999) and believed as most accurate to date.
Kabashima Yoshiyuki
Mourik Jort van
Nakamura Kazutaka
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