We assess a digital post-compensation method based on the backward propagation of the received signal to estimate the originally transmitted message. We developed a single channel baseband simulation model and used a symmetric and non-iterative version of the split-step Fourier method for solving the nonlinear Schrödinger equation describing the backward propagation. Using an NRZ-QPSK modulation format we obtained numerous simulation results under different test conditions and thereby showed that this method allows the joint compensation
of linear and nonlinear impairments in fiber. We also presented heuristics for the split-step Fourier method step-size, number of samples per symbol and optimal dispersion maps that optimize the tradeoff between performance and computational requirements for digital compensation.