## 5 The CDS case study for the OFDM-Based Long-Haul Standard Single-Mode Fiber system
It is customary to project the Q-factor based on BER and Gaussian noise statistics as [33; 42; 43]:  
\[Q=20 log10\Big{(}\sqrt{2}erfcinv(2.BER)\Big{)} \tag{9}\]  
In Figure 18, the Q-factors of the conventional system, CDS in BER improvement mode, and CDS in prediction mode for the data rate of 54 Gb/s (\(k\) = 4) as the function of the launch power are compared. As can be seen, the Q-factor improves by 1.75 and 2.74 dB when the CDS operates in prediction mode and BER improvement mode, respectively. The improvement in BER using the CDS principle is due to the Bayesian approach, while the data rate enhancement is due to the cycling through the prediction mode and BER improvement mode. From Figure 18, it may be noted that the optimum launch power does not change for the case of CDS in BER improvement mode as compared to the conventional system, although it increases slightly in the prediction mode (blue curve). However, if DBP is used in a conventional system, then the optimum launch power increases. This is because the DBP compensates for nonlinear impairments to some extent. The simplified CDS in this example should not be considered as a substitute for a nonlinear compensation scheme such as DBP. The difference between the DBP or any nonlinear compensation scheme and our approach is that the DBP makes use of the deterministic channel model (such as nonlinear Schrodinger equation) whereas our approach utilizes the statistical channel model. The Q-factor gain shown in Figure 18 using the simplified CDS is due to the information extracted by the perceptor that helps the CDS to approximate the optimal decision-making boundaries even if the symbol likelihood is non-Gaussian and asymmetric. Therefore, the final data rate is fixed at 54 Gb/s. Additionally, for distances less than 1600 km, we note that the CDS allows sending a signal without coding [44] (soft decision overhead), since the Q-factor is close to the forward-error correction limit (6.75% overhead for hard decision) [40]. Therefore, this reduces the FEC computational cost if the system uses the adaptive FEC and improves data rate efficiency. This Q factor improvement  
Figure 18: The simulation results for the quality-factor versus launch power for the conventional system, CDS prediction mode, and CDS improvement mode. makes the system less sensitive to any small disturbance, and the system will have better QoS with less interruptions. Using the proposed CDS, the BER can be improved further by operating the preceptor in the BER improvement mode with a lower PF (see Figure 11). However, this is not implemented in the example described here. We have provided an example of how a CDS with a simple executive CDS can still improve the BER, increase the data rate and handle changes in fiber optic channel with less interruption. A complex executive with a combination of different types of actions is still under investigation. From Figures 16-18, it may be noted that as the signal power increases, the BER gets larger due to fiber nonlinear impairments. Therefore, the advanced executive should take some advanced actions such as probabilistic shaping or geometric shaping to mitigate the nonlinearity. For example, the CDS can still improve the Q-factor by 3 dB at 0 dBm launch power (Figure 18). However, the Q-factor of 4.2 dB at 0 dBm launch power is below the FEC threshold. Therefore, CDS with advanced actions will be implemented in our future work.