An analytical discrete-time model is introduced for single-wavelength polarization multiplexed nonlinear fiberoptical channels based on the symmetrized split-step Fourier method (SSFM). According to this model, for high enough symbol rates, a fiber-optic link can be described as a linear dispersive channel with additive white Gaussian noise (AWGN) and a complex scaling. The variance of this AWGN noise and the attenuation are computed analytically as a function of input power and channel parameters. The results illustrate a cubic growth of the noise variance with input power. Moreover, the cross effect between the two polarizations and the interaction of amplifier noise and the transmitted signal due to the nonlinear Kerr effect are described. In particular, it is found that the channel noise variance in one polarization is affected twice as much by the transmitted power in that polarization than by the transmitted power in the orthogonal polarization. The effect of pulse shaping is also investigated through numerical simulations. Finally, it is shown that the analytical performance results based on the new model are in close agreement with numerical results obtained using the SSFM for a symbol rate of 28 Gbaud and above.

Abstract-Rate-adaptive optical transceivers can play an important role in exploiting the available resources in dynamic optical networks, in which different links yield different signal qualities. We study rate-adaptive joint coding and modulation, often called coded modulation (CM), addressing non-dispersion-managed (non-DM) links, exploiting recent advances in channel modeling of these links. We introduce a four-dimensional CM scheme, which shows a better tradeoff between digital signal processing complexity and transparent reach than existing methods. We construct a rate-adaptive CM scheme combining a single low-density paritycheck code with a family of three signal constellations and using probabilistic signal shaping. We evaluate the performance of the proposed CM scheme for single-channel transmission through long-haul non-DM fiber-optic systems with electronic chromaticdispersion compensation. The numerical results demonstrate improvement of spectral efficiency over a wide range of transparent reaches, an improvement over 1 dB compared to existing methods.Index Terms-Fiber-optic communications, four-dimensional set partitioning, non-dispersion managed links, nonlinear channel model, probabilistic shaping, rate-adaptive coded modulation.

Abstract-In this paper, the statistics of received signals in a single-channel dispersion-managed dual-polarization fiber-optical channel are derived in the limit of low dispersion. The joint probability density function (pdf) of the received amplitudes and phases of such a system is derived for both lumped and distributed amplification. The new pdf expressions are used to numerically evaluate the performance of modulation formats over channels with nonlinear phase noise. For example, a sensitivity gain of up to 2 dB is calculated for a specific system using polarization-multiplexed 8-ary phase shift keying compared with a similar single-polarization system at the same spectral efficiency and a symbol error rate of 5 × 10 −4 . Moreover, the accuracy of the derived pdf is evaluated for some single-channel dispersionmanaged fiber-optical links with different dispersion-maps using the split-step Fourier transform method.

Coherent optical transmission systems naturally lead to a four dimensional (4D) signal space, i.e., two polarizations each with two quadratures. In this paper we derive an analytical model to quantify the impact of Kerr nonlinearity on such 4D spaces, taking the interpolarization dependency into account. This is in contrast to previous models such as the GN and EGN models, which are valid for polarization multiplexed (PM) formats, where the two polarizations are seen as independent channels on which data is multiplexed. The proposed model agrees with the EGN model in the special case of independent two-dimensional modulation in each polarization. The model accounts for the predominant nonlinear terms in a WDM system, namely self-phase modulation and and cross-phase modulation. Numerical results show that the EGN model may inaccurately estimate the nonlinear interference of 4D formats. This nonlinear interference discrepancy between the results of the proposed model and the EGN model could be up to 2.8 dB for a system with 80 WDM channels. The derived model is validated by splitstep Fourier simulations, and it is shown to follow simulations very closely.

We evaluate the impact of variable-code-rate transceivers on cost, capacity and survivability of wavelengthrouted optical networks. The transmission rate and reach tradeoff is quantified for two hypothetical coded modulation schemes (aggressive and conservative) in a wavelength routing network with 50-GHz-spaced channels. The aggressive scenario assumes the 64-QAM modulation format, a small gap to capacity, and a small excess bandwidth. The conservative scenario considers the 16-QAM modulation format, and a larger capacity gap and excess bandwidth. The performance of the conservative and aggressive technologies is evaluated in three representative networks. Transparent reaches are calculated by means of an existing analytical method which assumes the AWGN hypothesis for the nonlinear noise. It is shown that variable-code-rate transceivers enable the concept of soft protection, in which the protection lightpath operates at a data rate which is lower than the corresponding working lightpath, in a way to avoid regeneration. This is specially attractive in the transport of IP traffic, where capacity reduction (in average up to 25%) may be tolerable during a repair time. It is also shown that variable-code-rate transceivers have the potential to offer significant savings in terms of transceiver usage and wavelength occupation, when compared to current fixed-rate transceivers operating at 100, 200 or 400 Gb/s. Finally, practical variable-code-rate transceivers may achieve a discrete set of N code rates, yielding a quantized capacity-versus-reach curve. The system impact of N is evaluated for several network scenarios.