Revisiting Binary Sequence Length Requirements to Accurately Emulate Optical Transmission Systems in Highly Dispersive Regime

When increasing channel bit rate beyond 10Gb/s or when operating over fiber lines with sparse or no in-line dispersion compensation, Kerr-like non-linear effects can be considered as second order with respect to dispersive effects, because pulse broadening can expand over numerous neighbor pulses, before optical non-linear effects imprint their signature noticeably. To accurately emulate the interactions between pulses in this case, a few studies emphasized that Pseudo- Random Binary Sequences (PRBS) should be used, with exponential dependence of the required PRBS length on bit rate and accumulated dispersion. In this paper, we explain our strategy to numerically estimate the required number of random, noisy bits for Monte-Carlo simulations, and show that it weakly increases in presence of pulse to pulse correlations and commonly tolerated levels of non-linearities (i.e. leading to transmission penalties as high as 1.5dB, for reference BERs of 10-2, 10-3 or 10-5) . Then we determine the actual required PRBS length that yields the same (sufficient) BER accuracy as the MC method. We demonstrate its actual dependence on BER, and show that MC theory provides a reliable upper bound in FEC-assisted, highly dispersive systems.