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Next-generation optical fiber systems will employ coherent detection to improve power and spectral efficiency, and to facilitate flexible impairment compensation using digital signal processors (DSPs). In a fully digital coherent system, the electric fields at the input and the output of the channel are available to DSPs at the transmitter and the receiver, enabling the use of arbitrary impairment precompensation and postcompensation algorithms. Linear time-invariant (LTI) impairments such as chromatic dispersion and polarization-mode dispersion can be compensated by adaptive linear equalizers. Non-LTI impairments, such as laser phase noise and Kerr nonlinearity, can be compensated by channel inversion. All existing impairment compensation techniques ultimately approximate channel inversion for a subset of the channel effects. We provide a unified multiblock nonlinear model for the joint compensation of the impairments in fiber transmission. We show that commonly used techniques for overcoming different impairments, despite their different appearance, are often based on the same principles such as feedback and feedforward control, and time-versus-frequency-domain representations. We highlight equivalences between techniques, and show that the choice of algorithm depends on making tradeoffs.