Misha Stepanov | publications | Phys. Rev. Lett. (2004)

V. Chernyak, M. Chertkov, M. G. Stepanov, B. Vasić, Error correction on a tree: An instanton approach, Physical Review Letters 93 (19) 198702 (2004).

DOI: 10.1103/PhysRevLett.93.198702
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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.