Error correction on a tree: an instanton approach.
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.
Chernyak
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Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA.
Chertkov
M
M
Stepanov
M G
MG
Vasic
B
B