In this paper, we investigate the use of the learned digital back-propagation
(LDBP) for equalizing dual-polarization fiber-optic transmission in
dispersion-managed (DM) links. LDBP is a deep neural network that optimizes the
parameters of DBP using the stochastic gradient descent. We evaluate DBP and
LDBP in a simulated WDM dual-polarization fiber transmission system operating
at the bitrate of 256 Gbit/s per channel, with a dispersion map designed for a
2016 km link with 15% residual dispersion. Our results show that in
single-channel transmission, LDBP achieves an effective signal-to-noise ratio
improvement of 6.3 dB and 2.5 dB, respectively, over linear equalization and
DBP. In WDM transmission, the corresponding $Q$-factor gains are 1.1 dB and 0.4
dB, respectively. Additionally, we conduct a complexity analysis, which reveals
that a frequency-domain implementation of LDBP and DBP is more favorable in
terms of complexity than the time-domain implementation. These findings
demonstrate the effectiveness of LDBP in mitigating the nonlinear effects in DM
fiber-optic transmission systems.

本文研究使用学习的数字背向传播（LDBP）来均衡分散管理（DM）链路中的双极化光纤传输，评估在 256 Gbit/s 每个通道的比特率下，采用频域实现的 LDBP 和 DBP 相对于线性均衡具有更高的信噪比增益。

利用学习的数字背向传播进行色散管理系统中的均衡化

Equalization in Dispersion-Managed Systems Using Learned Digital  Back-Propagation

Digital back-propagation (DBP) and learned DBP (LDBP) are proposed for
nonlinearity mitigation in WDM dual-polarization dispersion-managed systems.
LDBP achieves Q-factor improvement of 1.8 dB and 1.2 dB, respectively, over
linear equalization and a variant of DBP adapted to DM systems.

该论文提出了数字反向传播（DBP）和学习 DBP（LDBP）用于减轻 WDM 双偏振色散管理系统中的非线性失真。LDBP 相较于线性均衡和一种适用于 DM 系统的 DBP 变种，分别实现了 Q 因子提高 1.8 dB 和 1.2 dB。

双极化色散管理系统的学习式数字背向传播

Learned Digital Back-Propagation for Dual-Polarization Dispersion Managed Systems

Fiber Kerr nonlinearity is a fundamental limitation to the achievable
capacity of long-distance optical fiber communication. Digital back-propagation
(DBP) is a primary methodology to mitigate both linear and nonlinear
impairments by solving the inverse-propagating nonlinear Schr\"odinger equation
(NLSE), which requires detailed link information. Recently, the paradigms based
on neural network (NN) were proposed to mitigate nonlinear transmission
impairments in optical communication systems. However, almost all neural
network-based equalization schemes yield high computation complexity, which
prevents the practical implementation in commercial transmission systems. In
this paper, we propose a center-oriented long short-term memory network
(Co-LSTM) incorporating a simplified mode with a recycling mechanism in the
equalization operation, which can mitigate fiber nonlinearity in coherent
optical communication systems with ultralow complexity. To validate the
proposed methodology, we carry out an experiment of ten-channel wavelength
division multiplexing (WDM) transmission with 64 Gbaud
polarization-division-multiplexed 16-ary quadrature amplitude modulation
(16-QAM) signals. Co-LSTM and DBP achieve a comparable performance of nonlinear
mitigation. However, the complexity of Co-LSTM with a simplified mode is almost
independent of the transmission distance, which is much lower than that of the
DBP. The proposed Co-LSTM methodology presents an attractive approach for low
complexity nonlinearity mitigation with neural networks.

本文提出了一种中心定向长短记忆网络（Co-LSTM）结合简化模式和回收机制的方法，以实现在具有超低复杂度的相干光通信系统中减轻纤维非线性。