In this work, we demonstrate the offline FPGA realization of both recurrent and feedforward neural network (NN)-based equalizers for nonlinearity compensation in coherent optical transmission systems. First, we present a realization pipeline showing the conversion of the models from Python libraries to the FPGA chip synthesis and implementation. Then, we review the main alternatives for the hardware implementation of nonlinear activation functions. The main results are divided into three parts: a performance comparison, an analysis of how activation functions are implemented, and a report on the complexity of the hardware. The performance in Q-factor is presented for the cases of bidirectional long-short-term memory coupled with convolutional NN (biLSTM + CNN) equalizer, CNN equalizer, and standard 1-StpS digital back-propagation (DBP) for the simulation and experiment propagation of a single channel dual-polarization (SC-DP) 16QAM at 34 GBd along 17x70km of LEAF. The biLSTM+CNN equalizer provides a similar result to DBP and a 1.7 dB Q-factor gain compared with the chromatic dispersion compensation baseline in the experimental dataset. After that, we assess the Q-factor and the impact of hardware utilization when approximating the activation functions of NN using Taylor series, piecewise linear, and look-up table (LUT) approximations. We also show how to mitigate the approximation errors with extra training and provide some insights into possible gradient problems in the LUT approximation. Finally, to evaluate the complexity of hardware implementation to achieve 200G and 400G throughput, fixed-point NN-based equalizers with approximated activation functions are developed and implemented in an FPGA.

翻译：本文展示了在相干光传输系统中，利用离线现场可编程门阵列实现基于循环神经网络和前馈神经网络的均衡器以补偿非线性的方法。首先，我们提出了一种实现流程，展示了将模型从Python库转换至FPGA芯片综合与实现的过程。随后，我们回顾了非线性激活函数硬件实现的主要替代方案。主要结果分为三部分：性能对比、激活函数实现方式分析以及硬件复杂度报告。在仿真与实验条件下，针对34 GBd单信道双偏振16QAM信号经17×70km大有效面积光纤传输的场景，我们给出了双向长短期记忆与卷积神经网络耦合均衡器、卷积神经网络均衡器以及标准1步每符号数字反向传播法在Q因子方面的性能表现。双向长短期记忆耦合卷积神经网络均衡器在实验数据集中取得了与数字反向传播法相近的结果，相较于色散补偿基线获得了1.7 dB的Q因子增益。此后，我们评估了使用泰勒级数、分段线性函数和查找表逼近神经网络激活函数时的Q因子及硬件资源占用影响。我们还展示了如何通过额外训练减轻逼近误差，并针对查找表逼近中可能出现的梯度问题提供了见解。最后，为评估实现200G和400G吞吐率时的硬件实现复杂度，我们在FPGA中开发并实现了采用近似激活函数的定点神经网络均衡器。