Error probability analysis of fiber optics channels in present of nonlinear phase noise

The theoretical analysis of bit error ratio (BER) of the bit-interleaved coded modulation (BICM) system depends on the probability density function (p.d.f) of log-likelihood ratios (L-values). However, the p.d.f of L-values do not have an analytic form for the fiber channels with nonlinear phase noise. In order to solve this problem, we introduce two estimators for the cumulant generating function (CGF) and its derivatives in this paper. The first estimator is directly from its definition. The second estimator is based on k-statistics. We conduct the numerical simulations to evaluate the performance of these two estimators. The numerical results show that, for matched decoding metric, the first estimator is consistent with the simulation results from low to high signal-to-noise (SNR) region whereas the second estimator is only valid from low to middle SNR region. For mismatched decoding metric, the saddlepoint deviates the expectation value of 0.5 and leads to unreliable results. With these estimators, the performance of a BICM system for fiber optic channels can be quickly evaluated without the implementation of coder and decoder.