## 3 Simulation and Data Center Experimental Results
### Experimental Setup and Results  
The performance of the LDPC-coded PS-NPS-8-PAM transmission in a fiber channel-based DWDM system was experimentally verified with the testbed depicted in Figure 6. Three 10 kHz-linewidth, continuous-wave, tunable sources (with the following center frequencies: \(f_{1}\) = 193.30 THz, \(f_{2}\) = 193.35 THz, and \(f_{3}\) = 193.40 THz) were coupled by an optical coupler and launched to a Mach-Zehnder modulator. The PRBS was sent to our LDPC-coded PS-NPS-8-PAM generator. Then, the LDPC-coded PS-NPS signals were sent to an arbitrary waveform generator (AWGen) to create 11.5 GBaud 8-PAM signals with a 66.7% FEC overhead, which meant the bit rate was 20.7 Gbps. After being converted to the optical domain by the modulator, the resulting signals were boosted by an erbium-doped fiber amplifier (EDFA) with a 6 dB noise figure. The enhanced signal was then sent to a \(1\times 3\) coupler to be split and interleaved into three fibers with different lengths (delay lines). The corresponding outputs were then applied to a \(32\times 32\) arrayed waveguide grating (AWG)-based datacenter network at three different input ports. Every input port worked as a selective bandpass filter. At the output port, we obtained three different center frequencies with different delays, which worked as our DWDM system. The output signal was then mixed with an amplified spontaneous emission (ASE) noise signal using a \(2\times 2\) coupler. We also employed a variable optical attenuator (VOA) after the ASE noise source to emulate the different optical SNR (OSNR) channel conditions. At the receiver side, the targeted frequency \(f_{2}\) was selected by a tunable filter (TF) and detected using a photodetector (PD). To collect the received baseband signal, we employed a 100 GS/s digital phosphor oscilloscope from Tektronix. Then, we performed offline digital signal processing (DSP) with the collected signals.  
Figure 5: BER performance for different ROF values for: (**a**) a PS distribution with an LDPC code of rate \(r\) = 0.8 and (**b**) a uniform distribution with an LDPC code of rate \(r\) = 0.6.  
The BER performance of the LDPC-coded PS-NPS-8-PAM is shown in Figure 7. We transmitted the PS-NPS-8-PAM signals with ROF = 0.8 and 1, and compared them against a PS-8-PAM. From this figure, we can see that when ROF = 1, it performed the same as the PS-8-PAM without NPS, which is because ROF = 1 will not change the pulse shape. On the other hand, when we set the ROF to 0.8, we obtained a 0.43 dB shaping gain improvement in OSNR at BER = \(10^{-5}\). In Figure 7, we compare the LDPC-coded PS- and uniform distribution-based schemes with both ROFs set to 0.8. We can see that uniform distribution required higher OSNRs, and we obtained a 1.1 dB shaping gain improvement in OSNR at BER = \(10^{-5}\).  
Figure 8 shows the comparison of BER performance between the LDPC-coded PS-NPS-8-PAM and LDPC-coded uniform distributed 8-PAM schemes. Evidently, the joint usage of PS and NPS could obtain a 1.27 dB OSNR improvement at BER = \(10^{-5}\) compared to the uniform signaling.  
Figure 6: Experimental data center setup. CP: coupler, DL: delay line.  
Figure 7: BER performance for: (**a**) a PS distribution with different ROFs and without NPS, and (**b**) a PS and uniform distribution comparison with the same ROF. OSNR: optical signal-to-noise ratio.