We investigate an improved digital back propagation (DBP) method based on a multi-stage perturbation theory to compensate for nonlinear impairments in fiber optic links. In the standard DBP, the nonlinear operation only calculates the phase shift based on the power of the current signal sample. In the proposed perturbation-assisted DBP (P-DBP) method, the nonlinear operation calculates nonlinear phase shifts and complex distortions taking into account the correlation among neighboring optical pulses, which significantly improves the accuracy of nonlinear calculation. We obtain analytical expressions to calculate the nonlinear phase shifts due to the self-phase modulation and intra-channel cross-phase modulation effects and the complex distortions due to the intra-channel four wave mixing effect. We experimentally demonstrate that in a 256-Gb/s polarization multiplexed system over a 2,000-km fiber optic link, the P-DBP method using 4 steps shows the same compensation performance as standard DBP using 40 steps. We perform algorithm complexity analysis and show that the P-DBP method reduces the computational complexity up to 82% as compared with the standard DBP for the same gain.