  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.
