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Summary form only given. Regeneration of soliton signals through synchronous phase or intensity modulation (PM or IM) causes dramatic reduction of jitter and amplitude noise, therefore enabling unlimited propagation distances. Through perturbation theory and extensive numerical simulations, it was shown that after regeneration, the output statistics of the jitter are non-Gaussian. In this paper, we derive through a simpler and analytical method the non-Gaussian probability density functions (PDF) for PM or IM. We use them to evaluate the respective deviations in bit error rates (BER) with respect to the Gaussian PDF approximation.