## 1 Introduction
Another approach is to use distributed Raman amplification using primary or secondary pumping or short-interval Raman amplification [9; 10; 11]. In this context, [PERSON] et al. proposed the introduction of dispersion elements co-located with OPC to improve symmetry by aligning regions where fiber nonlinearity has a significant influence on the same cumulative dispersion [12]. The authors of this paper also proposed and verified the various MSSI-based DM links as the link technology for CD and nonlinear distortion compensation of 960 Gb/s WDM signals [13; 14; 15]. In applying the DM link to the MSSI system, the most important thing to prioritize to satisfy the dispersion-power symmetry condition is to ensure that the cumulative dispersion profile versus the transmission distance, i.e., the dispersion map, is symmetrical around the midway-OPC. We have confirmed that antipodal symmetry is more effective in compensating for distortion in the WDM channel than bilateral symmetry with respect to midway-OPC [13]. However, to form an antipodal-symmetric dispersion map, the lengths and dispersion coefficients of SMF and DCF consisting of the optical fiber span must be selected and distributed artificially and regularly. The amount of dispersion accumulated for each optical fiber span constructing the dispersion map is defined as residual dispersion per span (RDPS). The RDPS is determined by the length and dispersion coefficient of SMF and DCF in the corresponding optical fiber span. In other words, the application of an antipodal symmetrical dispersion map to the DM link means that the RDPS of all optical fiber spans is artificially allocated under special rules. Consequently, the method of artificially selecting and allocating RDPS improves the performance of WDM channels but also limits the diversity of link designs. The design rule in which the RDPS of each optical fiber span is randomly determined is most desirable in terms of flexibility in DM link design. However, due to the random distribution of RDPS, it is difficult to symmetrize the dispersion profile with respect to the midway OPC, so it is predicted that less than excellent compensation will be obtained. In a previous study, the authors proposed the MSSI-based DM link with the dispersion map composed of random-based RDPS [15]. As a result of numerical analysis of those dispersion maps, it was confirmed that among the three proposed methods of arranging the random RDPSs, the 'random-inverse' configuration provides the most effective compensation. The 'random-inverse' scheme is a method in which the RDPS of the optical fiber spans constituting the front section of the midway-OPC are randomly selected, and at the same time, the arrangement order of the RDPS of the optical fiber spans in the rear section is artificially reversed. This scheme is based on the random distributed RDPSs and makes the dispersion map antipodal-symmetric because the RDPS arrangement before and after midway-OPC is opposite to each other. In other words, we have confirmed that this scheme can satisfy both the improvement of link flexibility and the system performance to some extent. The sign and magnitude of the randomly selected RDPS were determined only by the length of the DCF in [15]. However, as mentioned earlier, the RDPS is determined by the correlation between the length and dispersion coefficient of the SMF and DCF in each optical fiber span. In other words, if the method of determining the sign and magnitude of the RDPS in the dispersion map of the 'random-inverse' scheme discussed in [15] is different, the degree of distortion compensation for the WDM signal may be different. In this paper, we numerically demonstrate the compensation characteristics of the WDM channels using different methods of determining the sign and magnitude of the RDPS in a 'random-inverse' dispersion map. The factors that change the sign and magnitude of the RDPS of the optical fiber span considered in this study are the DCF length and SMF length, respectively.