In the last few years, research in high-capacity transmission has shifted to coherent detection.  Advances in digital signal processing (DSP) have enabled phase and polarization management required for coherent detection in the electrical domain.  Moreover, coherent detection in conjunction with DSP enables compensation of fiber-optic transmission impairment, opening up new possibilities that will likely shape the future of optical transmission technology. Recently, digital backward propagation (DBP) has been proposed for the compensation of fiber impairments. The implementation of DBP consists on solving the z-reversed propagation equations that describe nonlinear transmission in fibers in the digital domain.  Provided that the channel characteristics are known, any deterministic effect can be pre/post-compensated at the transmitter/receiver. The joint compensation of dispersion and nonlinearity allows significant increase in launch power to values beyond the traditional nonlinear limit. As a result, higher OSNR and thus higher spectral efficiency and/or longer transmission reach can be achieved.   Despite its proven efficacy in both improving performance and extending reach, DBP is still challenging in terms of DSP complexity.  We will show that it is possible to reduce the computational load required for nonlinearity compensation to a practical level.