Error correction on a tree: An instanton approach

An error-corrected code with a uniform variable and/or check node degree distribution, was discussed. The generic method that applied to a variety of error-correction schemes in the regimes where low BER was illustrated. The sequence of transitions suggested a substantial flattening of the BER dependence on the signal-to-noise (SNR) ratio at moderate values of the latter. It was found that rise in SNR led to decrease in the symmetry of the phase dominating BER.