Accuracy Assessment of Nondispersive Optical Perturbative Models through Capacity Analysis

Abstract

A number of simplified models, based on perturbation theory, have been proposed for the fiber-optical channel and have been extensively used in the literature. Although these models are mainly developed for the low-power regime, they are used at moderate or high powers as well. It remains unclear to what extent the capacity of these models is affected by the simplifying assumptions under which they are derived. In this paper, we consider single-channel data transmission based on three continuous-time optical models: (i) a regular perturbative channel, (ii) a logarithmic perturbative channel, and (iii) the stochastic nonlinear Schrödinger (NLS) channel. To obtain analytically tractable discrete-time models, we consider zero-dispersion fibers and a sampling receiver. We investigate the per-sample capacity of these models. Specifically, (i) we establish tight bounds on the capacity of the regular perturbative channel; (ii) we obtain the capacity of the logarithmic perturbative channel; and (iii) we present a novel upper bound on the capacity of the zero-dispersion NLS channel. Our results illustrate that the capacity of these models departs from each other at high powers because these models yield different capacity pre-logs. Since all three models are based on the same physical channel, our results highlight that care must be exercised in using simplified channel models in the high-power regime.

Regular perturbation on the group-velocity dispersion parameter for nonlinear fibre-optical communications

“…c RP on γ model given by (15). d RP on β 2 model given by (19). Each model has a different accuracy, measured in NSD, for a specific set of input powers, β 2 coefficient, and distance.…”

“…This assumption was used in the literature, for example, when chromatic dispersion is completely compensated 18 . The same premise was considered when analysing the highly nonlinear regime, i.e., when the nonlinearities are predominant and may be an important effect to take into account 12,19 . As will be seen in the Results section, even in that regime the dispersion can deteriorate the performance of the model.…”

Path Integral Approach to Nondispersive Optical Fiber Communication Channel

“…Another type of the models is considered in Refs. [ 4 , 17 , 18 , 19 , 20 , 21 , 22 ], where it is assumed that the amplifiers are continuously distributed in such a way that there is no attenuation, but the amplifiers induce the stochastic noise in the channel. Below we consider this type of model.…”

“…In Refs. [ 4 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ] the propagation of the signal is described by the NLSE with zero dispersion, therefore, the signal propagation at different time moments evolves independently. So, formally, one can consider the signal in the fixed time moment, and the signal ceases to depend on time.…”

“…Using the method we find the probability density function of the input signal that maximizes the mutual information obtained in the leading order in the parameter in the intermediate power range. In the recent paper [ 22 ] the important result was obtained: the authors found the upper bound of the capacity for the per-sample model for arbitrary signal powers. The results of Refs.…”