An adaptive coding scheme for nonlinear channels improves reliability and an efficiency in digital communication networks. The method monitors channel statistics to analyze an extrinsic information transfer chart of the channels. The channel statistics are fed back to the transmitter to adapt forward error correction coding. A parametric analysis method uses a Gaussian mixture model. The statistical information feedback can adapt an ARQ sheme by adding a weighted received signal to the original coded signals to reduce nonlinear distortion. Trellis shaping can make the transmitting signal preferable for nonlinear channels.