## 5 Conclusions  
Up to now, we have numerically investigated the effect of the factor of determining RDPS on the compensation for the distorted WDM signals in the 'random-inverse' schemed DM link. The factors that determine the randomly selected RDPS sign and magnitude are the SMF length and DCF length, which make up the optical fiber span. In other words, we analyze the distortion compensation of 960 Gb/s WDM signals in the case where the DCF length (or SMF length) of all optical fiber spans varies randomly in the front section before the midway OPC. It was confirmed that the method of determining the random-based RDPS by varying the DCF length generally improved the compensation effect of the distorted WDM channel compared to the case of varying the SMF length. This result is to inform that DCF has a slightly greater impact than SMF in determining RDPS, which is an important element of inline DM link configuration. The length of DCF, which plays a role in controlling RDPS in inline DM links, is usually shorter than the SMF length due to its large dispersion coefficient. The degree of variation of each fiber length to make the same RDPS is the same for the reference lengths of 80 km for SMF and 16 km for DCF. However, the variation ranges of optical fiber length corresponding to the same RDPS change between adjacent optical fiber spans is larger in SMF than in DCF, and in particular, as the RDPS change becomes more severe, the variation degree of SMF length becomes larger. The authors believe that because of this feature, the random-based RDPS determination by DCF length variation enables somewhat improved compensation than by SMF length variation. It is thought that the dramatic difference in optical fiber length in consecutive fiber spans may ultimately have a negative effect on the compensation. Our current study was conducted following the results of previous research by [15]. In other words, the biggest reason why the compensation performance in most of the 50 random patterns considered was superior to the 'non-random fixed' dispersion map is because the 'random-inverse' schemed DM link, which can obtain the best compensation among the methods for randomly selecting RDPS in the previous research [15], was used. Here, the 'random-inverse' schemed DM link is meaningful in terms of compensation efficiency for distorted WDM channels because it is based on the MSSI system. What the authors want to emphasize is not that good compensation is achieved in most of the random patterns considered. Instead, among the dispersion maps that form 'random-inverse' schemed DM links through random-based RDPS, there are characteristics of random patterns that can achieve excellent compensation, and these characteristics should be utilized when designing the exact DM links. We believe that this is one of the implications of this paper. If the parameters that consist of the DM link have random values, it is very difficult to evaluate performance through analytical methods. This means that finding the random arrangement that results in the best and worst performance is only possible through numerical simulation. Accordingly, we derived the performance of all 50 random patterns through numerical simulation and compared and analyzed each result to find a specific pattern that could improve WDM compensation performance. Strictly speaking, this paper does not have high academic originality because it is based on the 'random-inverse' schemed DM link with random-based RDPS evaluated in previous research. However, through this paper, there was a meaningful performance comparison as a function of the method for determining the random-based RDPS, and the characteristics of the RDPS random pattern that forms the dispersion map that may be more advantageous for improving compensation performance were derived. We hope that the random-based dispersion maps proposed in this paper, its analysis method, and the induced results from performance evaluation will be helpful in designing the DM links combined with the MSSI system. Conceptualization, J.-P.C.