We study the post nonlinearity compensation of differential-phase-shift-keying links employing pure soliton transmissions over a large number of spans.In addition to the distributed amplified spontaneous noises added by the inline amplifiers,lumped intensity noises initially resulting from transmitter imperfections are also considered.Based on the soliton perturbation theory,we derive simple and accurate formulae for the optimum operating phase,the variance of the residue phase noise,and the phase Q-factor improvement of the post nonlinearity compensation.We validate these derived formulae by comparing their results with numerical simulations built upon the split-step Fourier method.