title: Error correction on a tree: an instanton approach.
abstract: We introduce a method that allows analytical or semianalytical estimating of the post-error correction bit error rate (BER) when a forward-error correction is utilized for transmitting information through a noisy channel. The generic method that applies to a variety of error-correction schemes in the regimes where the BER is low is illustrated using the example of a finite-size code approximated by a treelike structure. Exploring the statistical physics formulation of the problem we find that the BER decreases with the signal-to-noise ratio nonuniformly, i.e., crossing over through a sequence of phases. The higher the signal-to-noise ratio the lower the symmetry of the phase dominating BER.
authors.affiliation: Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA.
authors.forename: V
authors.initials: V
authors.lastname: Chernyak
authors.forename: M
authors.initials: M
authors.lastname: Chertkov
authors.forename: M G
authors.initials: MG
authors.lastname: Stepanov
authors.forename: B
authors.initials: B
authors.lastname: Vasic