## 2 Experimental Setup  
The experimental implementations used to obtain the results of this paper are shown in Figure 1a,b. In Figure 1a, at the transmitter side, an arbitrary waveform generator (AWG) is used to provide a high integrity electrical signal. The AWG offers a bandwidth of 30 GHz and operates at 84 GS/s. Because of the AWG's inherent hardware bandwidth limitations, signal pre-distortion is applied at the transmitter to compensate for it; i.e., the frequency response of the AWG is measured, and the inverse function is applied to the data to achieve a quasi-flat frequency response. The PAM-4 signal is generated in Matlab using a pseudo-random binary sequence (PRBS) of length \(2^{15}-1\) that is mapped to the corresponding PAM-4 symbols. The obtained symbol sequences are then downloaded to the AWG, and a 330 mV peak-to-peak 28 Gbd PAM-4 signal is generated at its output, shown as inset (i) in Figure 1a. The electrical signal is adjusted in amplitude by an RF attenuator in line with a microwave amplifier. The electrical signal at the output of the RF amplifier (shown as inset (ii) in Figure 1a) is then used to drive the EML. Both the driving amplitude and the bias point of the EML are optimizedto achieve the optimum performance under each transmission scenario. The output of the EML is approximately 0 dBm. A temperature controller is used to stabilize the operating point of the EML during the experiments. The 56 Gb/s PAM-4 optical signal at the output of the EML is then launched over standard single mode fiber spools of length 10-km, 15-km, 20-km, 25-km, and 30-km SSMF. The signal is detected on a 22-GHz p-i-n photodiode (PD) with integrated TIA. An EDFA is used in the link only to enable transmission higher that 25 km. The received optical power is varied before the receiver by a variable optical attenuator (VOA), and the optical power is monitored on a power-meter (PM) to test the BER transmission performance of the 56 Gb/s PAM-4 signal. Note that in order to evaluate the tolerance of our proposed scheme in the presence of CD, no dispersion compensation module is employed in the link. Next, the photocurrent is sampled on a real-time scope with channel bandwidth 33 GHz operating at 80 GS/s, and the data samples are stored and processed offline using the DSP blocks shown in Figure 1c. In the DSP part, first the signal is re-sampled to two samples per symbol and the amplitude is adjusted using an automatic gain control block (AGC) to enable appropriate convergence of the FIR equalizer. Then, timing recovery is performed [17] in order to compensate for timing drifts of the symbols, and next a hybrid implementation of an FIR equalizer followed by an MLSE block is employed to remove the inter-symbol interference induced by the chromatic dispersion in the link and decide on the transmitted symbol [18; 19]. The BER is calculated at the output of both the FIR and the MLSE; BER is also calculated for the case when only an MLSE is employed to infer on its necessity at the input of the MLSE. We also investigate a second experimental configuration that employs a lower bandwidth transmitter (i.e., 15-GHz DAC), originally presented in [15], shown in Figure 1b. Results for back-to-back and after transmission over 10-km, 15-km, 20-km, 25-km, and 30-km are obtained in order to compare the performance of the two schemes shown in Figure 1a,b.