## 2 Operation Principle of the Proposed NN-Based Equalization Scheme
In particular, the random data are applied into all the measurements to avoid the overestimation with the use of a PRBS. The cycle length of the random data is 10,000. There are 16 neural nodes in each layer. The network is trained with back-propagation and gradient descent with Adam optimization. In this work, the neural network can get the relationship between the adjacent symbols and get the correct data by extending the dimension of the data through delay processing. Compared with the traditional linear equalizer, besides the basic equalization ability, the hidden layer of the network enhances the learning ability, and the activation function enhances the expression ability, so it has the potential to obtain a better equalization effect especially in the multi-mode, non-linear, and other complex transmission environments. Figure 2: (**a**) The schematic diagram of delay and (**b**) the algorithm flowchart of the proposed NN equalizer. The experimental setup for evaluating the performance of the proposed equalization scheme is illustrated in Figure 3. At the transmitter side, the random data are generated and mapped into the PAM-4 format by Matlab, and then they are sent to the Keysight M8196A arbitrary waveform generator (AWG) for electric signal generation. The sampling rate of the AWG was 92 GS/s and the corresponding bandwidth was 30 GHz. The eye diagram of the 100 Gb/s electrical PAM-4 signal emitting from the AWG (point a) without optoelectronic and electro-optical devices is also shown in Figure 3a, in which case the eyes are clearly visible. Since the maximum output voltage of the AWG was only 500 mV, a broadband electric amplifier with 55 GHz bandwidth was connected to the AWG to amplify the voltage. An 850 nm Fabry Perot (FP) laser was employed and followed by a 25 G 850 nm Mach-Zehnder modulator (MZM), which was provided by Bonphot (850 MODBOX). A polarization controller was not included in our experimental setup because polarization while maintaining optical fiber was used for connecting the laser source and the MZM. The insertion loss of the MZM was 4.5 dB, the optical output power of the laser source was 11 dBm, and the corresponding optical power injected into optical backplane was around 6.5 dBm. After 40 cm optical backplane transmission, the RoP was adjusted by a variable optical attenuator (VOA). At the receiver side, the optical signal was detected by a 22 G positive intrinsic-negative (PIN) detector. The detected signal was then sampled by an 80 GS/s real-time digital storage oscilloscope (DSO) with a 33 GHz bandwidth to obtain the data for offline analysis. The eye diagram of the 100 Gb/s electrical PAM-4 signal output from PIN after the 40 cm optical backplane (point b) is also depicted in Figure 3, which shows that the quality of the eye diagram was very poor. An offline digital signal processing (DSP) is executed by the Matlab program, and this procedure is shown in Figure 3. The sampled data from the DSO were first resampled to make sure that there were integer symbols in the sampling period. Then, the optimal sampling point was obtained based on the absolute-value timing symbol recovery algorithm. After the equalization, the BER was then calculated for the evaluation of the system performance. Two types of common equalization schemes including DFE and MLSE were considered for comparative analysis. The optical backplane employed in the present experiment was in-house fabricated, with its specific parameters shown in reference [26]. As shown in Figure 4, a total of 10 rectangular optical waveguides (ROWs) were embedded in the substrate of the optical backplane. Two ends of the waveguide were coupled to the optical multi-mode 1 (OM1) MMF from the substrate by using dedicated connectors. The cross-sectional view of one of the ROWs is also provided in Figure 4, where the refractive index of the core is shown to have been 1.4662, slightly higher than that of the cladding (1.45).