## 1 Introduction  
In the last few years, worldwide traffic in telecommunication networks has been increasing dramatically around \(30\%\) per year [1, 2]. This growth is fueled by the progressive development of next-generation 5G mobile broadband technologies, expansion of the Internet of Things, and increasing of high data-rate applications such as streaming video, real-time gaming, cloud computing, and big data analysis [3]. To accomplish this capacity growth, in recent years, datacenters owned by cloud companies and content providers have proliferated around the world to provide increased availability, high bandwidth and reduced latency to customers [4]. Moreover, the major amount of traffic is now exchanged between servers inside the same datacenter and between datacenters [1]. Datacenters interconnect (DCI) technology has evolved and continues to evolve to support this data capacity growth. In short intra-datacenter links, the format of the transmitted signals was usually the on-off keying (OOK), where intensity-modulation and direct-detection (IM-DD) ensured low cost and reduced complexity [5]. However, in 2014, OOK signal transmission reached its limit at the data rate of \(25\) Gb/s [6]. To surpass this limitation, four-level pulse amplitude modulation (PAM4) signal transmission has been deployed for DCI communications in 2017 with the target of improving data capacity [5, 7]. The PAM4 format doubles the spectral efficiency in comparison to OOK, and is expected to be an economical and efficient enabler of \(100\)G and \(400\)G single-channel transmission in intra-DCI and inter-DCI links [5, 6]. Multi-core fibers (MCFs) can improve even further the capacity of DCI links, while saving space inside datacenters in comparison with the space occupied by the large number of single-mode single-core fibers (SM-SCF) required to achieve the same capacity [8]. Weakly-coupled MCFs are a good solution to achieve the required capacity, since the individual cores can be used independently for data transmission with similar latency. However, the reach and transmission performance with weakly-coupled MCFs is impaired by a physical intrinsic phenomenon known as inter-core crosstalk (ICXT) [2; 9; 10]. The ICXT has been characterized in several works [9; 10; 11; 12; 13; 14; 15; 16]. In particular, the dual-polarization discrete changes model (DP-DCM) has been proposed in [13] to describe the distribution of ICXT field by the two polarizations. This model has been validated by experimental results of short-term average ICXT, the autocovariance of the ICXT power, decorrelation bandwidth of the ICXT power, stochastic time characterization of the short-term average ICXT and autocovariance of the short-term average ICXT [10; 14; 15; 16]. Due to the random evolution of ICXT over time, the ICXT can lead to: (i) random fluctuations of the bit error rate (BER) over short time periods [17; 18], and (ii) system outage over long time periods of high ICXT power [17; 19]. It has been shown that, in IM-DD systems, periods with high ICXT power are more likely to occur due to the random evolution of ICXT [12]. Therefore, the evaluation of the system outage, through the outage probability (OP) metric, is of utmost importance to assess the performance of IM-DD links supported by MCFs. The ICXT impact on the OOK system performance has been assessed by comparing experimental and simulated BERs and OPs in weakly-coupled MCFs [19] and by comparison with theoretical results [20]. The dependence of the OP due to ICXT on several parameters and features of OOK systems, such as the laser linewidth [21], skew-symbol rate product [21; 22], and ICXT level [19; 22] has been studied. The impact of ICXT on the performance of PAM4 IM-DD systems has also been assessed [23; 24; 25; 26]. The dependence of the BER on the received power has been assessed experimentally in an unamplified 2 km link with 100 Gb/s PAM4 signals and in an unamplified 2.5 km link with 112 Gb/s to show the system feasibility in the presence of ICXT [23; 24].