In this paper, probabilistic shaping is numerically and experimentally investigated for increasing the transmission reach of wavelength division multiplexed (WDM) optical communication systems employing quadrature amplitude modulation (QAM). An optimized probability mass function (PMF) of the QAM symbols is first found from a modified Blahut-Arimoto algorithm for the optical channel. A turbo coded bit interleaved coded modulation system is then applied, which relies on manyto-one labeling to achieve the desired PMF, thereby achieving shaping gains. Pilot symbols at rate at most 2% are used for synchronization and equalization, making it possible to receive input constellations as large as 1024QAM. The system is evaluated experimentally on a 10 GBaud, 5 channels WDM setup. The maximum system reach is increased w.r.t. standard 1024QAM by 20% at input data rate of 4.65 bits/symbol and up to 75% at 5.46 bits/symbol. It is shown that rate adaptation does not require changing of the modulation format. The performance of the proposed 1024QAM shaped system is validated on all 5 channels of the WDM signal for selected distances and rates. Finally, it is shown via EXIT charts and BER analysis that iterative demapping, while generally beneficial to the system, is not a requirement for achieving the shaping gain.

This paper reviews digital signal processing techniques that compensate, mitigate, and exploit fiber nonlinearities in coherent optical fiber transmission systems. References and links1. A. Mecozzi and R.-J. Essiambre, "Nonlinear Shannon limit in pseudolinear coherent systems," J. Lightw. Technol. 2011-2024 (2012). 2. A. Mecozzi, C. B. Clausen, and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12(4), 392-394 (2000). 3. L. Dou, Z. Tao, L. Li, W. Yan, T. Tanimura, T. Hoshida, and J. C. Rasmussen, "A low complexity pre-distortion method for intra-channel nonlinearity," in Optical Fiber Communication Conference (2011), paper OThF5. 4. Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, "Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate," J. Lightw. Technol. 29(17), 2570-2576 (2011). 5. T. Oyama, H. Nakashima, S. Oda, T. Yamauchi, Z. Tao, T. Hoshida, and J. C. Rasmussen, "Robust and efficient receiver-side compensation method for intra-channel nonlinear effects," in Optical Fiber Communication Conference (2014), paper Tu3A.3. 6. A. Ghazisaeidi, I. Fernandez de Jauregui Ruiz, L. Schmalen, P. Tran, P. Brindel, C. Simonneau, E. Awwad, B. 30(12),Uscumlic, P. Brindel, and G. Charlet, "Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction," IEEE/OSA J. Lightw. Technol. 34(8), 1886-1895 (2016 Vol. 25, No. 3 | 6 Feb 2017 | OPTICS EXPRESS 1918 eigenvalue division multiplexing in optical fiber channels," Phys. Rev. Lett. 113(1), 013901 (2014

A new geometric shaping method is proposed, leveraging unsupervised machine learning to optimize the constellation design. The learned constellation mitigates nonlinear effects with gains up to 0.13 bit/4D when trained with a simplified fiber channel model.

In this letter, the fiber-optic communication channel with a quadrature amplitude modulation (QAM) input constellation is treated. Using probabilistic shaping, we show that high-order QAM constellations can achieve and slightly exceed the lower bound on the channel capacity, set by ring constellations. We then propose a mapping function for turbocoded bit-interleaved coded modulation based on optimization of the mutual information between the channel input and output. Using this mapping, spectral efficiency as high as 6.5 bits/s/Hz/polarization is achieved on a simulated single channel long-haul fiber-optical link excluding the pilot overhead, used for synchronization, and taking into account frequency and phase mismatch impairments, as well as laser phase noise and analog-to-digital conversion quantization impairments. The simulations suggest that major improvements can be expected in the achievable rates of optical networks with high-order QAM.

The rate flexibility and probabilistic shaping gain of 4-dimensional signaling is experimentally tested for short-reach, unrepeated transmission. A rate granularity of 0.5 bits/QAM symbol is achieved with a distribution matcher based on a simple look-up table.

The nonlinear Fourier transform is a new approach of addressing the capacity limiting Kerr nonlinearities in optical communication systems. It exploits the property of integrability of the lossless nonlinear Schrödinger equation and thus incorporates nonlinearities as an element of the transmission. However, practical links employing erbium-doped fiber amplifiers include losses/gains and introduce noise which breaks the integrability of the nonlinear Schrödinger equation. Although the lossless path average approximation proposes an integrable model, its imprecision still leads to unintended distortions and thus performance degradation. We propose an alternative receiver for nonlinear frequency division multiplexing optical communication systems using techniques from machine learning. It is highly adaptive as it learns from previously transmitted pulses and thus holds no assumptions on the system and noise distribution. The detection method presented is fully applied in time-domain and omits the nonlinear Fourier transform. The numerical results provide a benchmark for nonlinear Fourier transform based detection of high order solitons for fiber links with losses and noise present.

Abstract-In this paper, we demonstrate wavelength conversion of advanced modulation formats such as 10-GBd 64-QAM and 256-QAM with high conversion efficiency over a 29-nm spectral window by using four-wave mixing in an AlGaAs-On-Insulator (AlGaAsOI) nano-waveguide. A thorough characterization of the wavelength converter is reported, including the optimization of the AlGaAsOI nano-waveguide in terms of conversion efficiency and associated bandwidth and the analysis of the impact of the converter pump quality and power as well as the signal input power. The optimized converter enables generating idlers with optical signal-to-noise ratio (OSNR) above 30 dB over a 29-nm bandwidth leading to error-free conversion of 64-QAM and 256-QAM with OSNR penalty below 1.0 dB and 2.0 dB respectively. The generated idlers exhibit an OSNR margin to the chosen forward error correction thresholds of >3 dB and >7 dB for 64-QAM and 256-QAM, respectively, that can be used for transmission after conversion.

Abstract-In this paper the problem of constellation shaping is considered. Mapping functions are designed for a manyto-one signal shaping strategy, combined with a turbo coded Bit-interleaved Coded Modulation (BICM), based on symmetric Huffman codes with binary reflected Gray-like properties. An algorithm is derived for finding the Huffman code with such properties for a variety of alphabet sizes, and near-capacity performance is achieved for a wide SNR region by dynamically choosing the optimal code rate, constellation size and mapping function based on the operating SNR point and assuming perfect channel quality estimation. Gains of more than 1dB are observed for high SNR compared to conventional turbo coded BICM, and it is shown that the mapping functions designed here significantly outperform current state of the art TurboTrellis Coded Modulation and other existing constellation shaping methods.