## 1 Introduction  
The capacity of optical communication links has increased exponentially since their introduction in the late 1970s [1]. This trend is expected to continue in the coming years, driven by new applications requiring high bandwidth, such as cloud computing, 5G/ 6G wireless, high-definition video streaming, and virtual reality [2]. In addition to these high-capacity issues, network services are becoming more dynamic and heterogeneous. However, there is growing recognition that this continued bandwidth demand will drive the required capacity closer to the maximum capacity theoretically predicted for that fiber [1]. Regarding the channel capacity of a transmission line, [PERSON] derived a specific closed-form expression for the capacity of an additive white Gaussian noise (AWGN) channel [3] that increases logarithmically with the signal-to-noise ratio. That is, for such a channel, the ultimate theoretical limit on transmission rate is determined only by the available signal power. Optical fiber behaves essentially like an AWGN channel at low signal powers. However, contrary to the case with AWGN, when the signal power is increased, the resulting nonlinearity damages existing systems to the point that they cease to operate at higher powers [3]. This naturally increases the impact of nonlinearity on the capacity of the optical fiber channel, and as signal power increases, the possibility that a finite limit on the capacity of the optical fiber channel actually exists increases, which is defined as the nonlinear Shannon limit (NSL) [3; 4]. Experiments based on various analytical expressions and simulation technologies have been attempted to overcome NSL, but no one has been able to show a system that overcomes it. These attempts were based on a variety of individual technologies, including third-window distributed feedback lasers (DFB), erbium-doped fiber amplifiers (EDFA), wavelength division multiplexing (WDM), forward error correction (FEC), and Raman amplification [1]. What is important to note here is that these individual technologies were generally accomplished in single-mode fiber (SMF)-based systems. To increase transmission capacity to approach NSL in an SMF-based transmission system, the link design technology that basically eliminates or reduces chromatic dispersion (CD) and nonlinearity is required. Two general approaches to compensating for CD are inline dispersion compensation (DC) and electronic DC [5]. Electronic DC uses digital signal processing (DSP) to compensate for signal distortion caused by CD. Inline DC, on the other hand, mitigates the effects of CD by adding passive optical components to each fiber span. Using a fiber Bragg grating (FBG) as the passive optical component eliminates the effects of CD locally within each wavelength division multiplexing (WDM) channel [6]. By inserting a dispersion-compensating fiber (DCF) into each fiber span, WDM can be compensated across the entire spectrum [5]. We call these two systems per-channel dispersion-managed (CDM) link and dispersion-managed (DM) link, respectively. Optical phase conjugation (OPC) is an optical signal processing technique to mitigate dispersion and Kerr effect-based nonlinear effects in SMF. By placing the OPC in the middle of a symmetrical link, the signal phase is conjugated, thereby inverting both the uniform dispersion and nonlinear effects due to Kerr in the second half of the link and providing the possibility of compensation [7]. A symmetrical link refers to a case where the dispersion-power profile is symmetrical with respect to the OPC location, and a system with the OPC located at the center of the symmetrical link is called mid-span spectral inversion (MSSI). There are some approaches to maximize symmetry in MSSI systems. One way is to use short span lengths that monotonically increase symmetry as spacing decreases. However, this increases the number of amplifiers required and initially reduces energy consumption [8], but the optimal spacing is a trade-off between energy consumption and symmetry.