## 4 Simulation Results and Discussion
That is, the design margin of the NRD and the launch power varies depending on the specific random pattern of the RDPS. Figure 7 shows the product and the maximum launch power that produces a 1-dB EOP for each pattern. In the result of Figure 7, the maximum launch power for pattern numbers 33 and 34 with similar product magnitudes are 4.2 and 5.2 dBm, respectively, with a difference of about 1-dB. This result means that in the dispersion-managed link designed with pattern number 33, the NRD can be generously selected as the maximum launch power and is lower compared to pattern number 34. Among the random-inverse distributions, the best product characteristic is obtained by applying pattern number 28, and since the  
Figure 6: The product of NRD and launch power. Figure 7: The product of NRD and launch power and the maximum launch power, which result in 1-dB EOP. (**a**) Random-inverse case, (**b**) random-follow case, and (**c**) all-random case. maximum launch power is not too large, NRD can be applied with sufficient margin. On the other hand, in the dispersion-managed link designed by pattern number 8, although the product characteristic is relatively good, it is difficult to apply NRD with the margin due to the relatively large maximum launch power. In conclusion, the RDPS pattern in the random-inverse distribution should be determined and applied according to the specific requirements such as NRD margin and power margin. Figure 8a shows the dispersion maps made with the RDPS distribution pattern that can obtain the best compensation among random-inverse distributions. On the other hand, Figure 8b shows the distribution maps made with the RDPS distribution pattern with the least compensation effect among the random-inverse distributions. Analyzing the dispersion maps shown in Figure 8a, it can be recognized that the amount of accumulated dispersion (i.e., positive values) and the amount of offsetting dispersion (i.e., negative values) is intensively large at the beginning and the end of the same transmission path. The optical pulse width in fiber spans in which the accumulated dispersion amount has a positive value is broader than the initial pulse width. As the width of the optical pulse is extended, the intensity of the optical pulse is weakened, and as a result, it is less affected by the nonlinear Kerr effect. However, if the cumulative dispersion is maintained only as positive value in all fiber spans in order to be less affected by the Kerr effect, inter-symbol interference (ISI) occurs due to the dispersion of optical pulses, which deteriorates the transmission quality. Therefore, it is necessary to make the cumulative dispersion amount negative at appropriate intervals. The dispersion maps shown in Figure 8a correspond to the shape following the aforementioned distribution of the accumulated dispersion. On the other hand, the dispersion maps shown in Figure 8b are also symmetric around the midway OPC but show different aspects from Figure 8a. In particular, the dispersion map generated by pattern number 43 has positive cumulative dispersion in the front part of the former half and negative cumulative dispersion in the rear part of the latter half, like the dispersion maps shown in Figure 8a. However, in this dispersion map, the overall shape of the accumulation and offset of the dispersion in each half link is generally wider than that in Figure 8a. Figure 8: The dispersion maps established by random-inverse distribution of RDPSs. (**a**) The best compensation cases, and (**b**) the worst compensation cases. The conclusion drawn from the analysis of Figure 8 is that effective compensation can result when the RDPS is randomly set to repeat the accumulation and offset of the dispersion in a relatively short period after the positive cumulative dispersion is concentrated at the beginning of the entire link. In addition to this, by setting the RDPS distribution order in the latter half link opposite to that in the former half, effective compensation can be obtained.