We propose a demodulation framework to extend the maximum distance of unrepeated transmission systems, where the simplest back propagation (BP), polarization and phase recovery, data arrangement for machine learning (ML), and symbol decision based on ML are rationally combined. The deterministic waveform distortion caused by fiber nonlinearity and chromatic dispersion is partially eliminated by BP whose calculation cost is minimized by adopting the single-step Fourier method in a pre-processing step. The non-deterministic waveform distortion, i.e., polarization and phase fluctuations, can be eliminated in a precise manner. Finally, the optimized ML model conducts the symbol decision under the influence of residual deterministic waveform distortion that cannot be cancelled by the simplest BP. Extensive numerical simulations confirm that a DP-16QAM signal can be transmitted over 240km of a standard single-mode fiber without optical repeaters. The maximum transmission distance is extended by 25km.