## 1 Introduction
The low latency of nested antiresonant nodeless fibers (NANFs) is particularly advantageous, primarily due to their effective refractive index, \(n_{\text{eff}}\approx 1\). However, several challenges must be addressed, such as the inability to perform Raman amplification within the transmission fiber, difficulties in interconnecting the SMF to the HCF or the HCF to the HCF, and fiber leakage issues, particularly in extreme environments such as deep-sea applications or highly urbanized areas exposed to extreme heat. HCFs also have a more rigid core structure compared to traditional solid core fibers, making them less flexible and more prone to microbending losses. This rigidity complicates installation and handling, especially in environments that require tight bends or complex routing. Furthermore, their delicate microstructured design makes HCFs more difficult to manipulate, splice, and terminate, requiring specialized equipment and techniques to minimize losses and maintain performance [11]. In latency-sensitive applications such as telemedicine or high-frequency trading [12], \(n_{\text{eff}}\) is not the only critical parameter. Beyond short-distance transmissions, where accumulated loss and dispersion (including chromatic dispersion and polarization mode dispersion) are within acceptable limits, it becomes crucial to employ streamlined transponders that minimize time-consuming signal processing tasks, such as forward error correction (FEC), dispersion compensation, and complex coding/decoding in modulation. Therefore, novel techniques are needed to ensure that the latency gains achieved with HCFs are not negated by processing overhead [11]. The use of burst pilots can significantly simplify the coding and decoding processes in modulation while maintaining the low-latency advantages of hybrid coding frameworks by reducing the signal processing burden. A key benefit of pilot symbol-based systems is their inherent reconfigurability, which enables seamless adaptation to various modulation formats. This flexibility is particularly valuable for phase recovery algorithms (e.g., MDE), which require modulation-specific adjustments. Additionally, an inherent advantage of using pilots is that they eliminate the need for differential encoding. In practical systems, differential encoding is often employed to address phase ambiguity, particularly when the absolute phase of the signal is unknown. However, its associated penalties must be carefully considered. Theoretical penalties for differential encoding have been calculated as 3 dB, 2.22 dB, 1.55 dB, and 1.04 dB for QPSK, 16 QAM, 64 QAM, and 256 QAM, respectively [13]. In the blind phase search (BPS) algorithm, differential encoding plays a critical role in resolving phase ambiguities that arise during phase estimation. BPS estimates the phase with potential ambiguities in multiples of \(\frac{2\pi}{M}\) for MQAM signals. The penalties for differential encoding in the BPS algorithm are reported as 0.7 dB, 0.6 dB, 0.5 dB, and 0.5 dB for QPSK, 16 QAM, 64 QAM, and 256 QAM, respectively [1]. Similarly, [14] reports penalties of 0.5 dB and 0.4 dB on a receiver BER of \(10^{-3}\) for set-partitioning 128 polarization-multiplexed 16 QAM (128-SP-QAM) and polarization-multiplexed 16 QAM (PM-16 QAM), respectively. The study in [15] investigates the impact of differential encoding on higher-order modulation formats and phase recovery. The authors highlight that differential coding is often employed to address cyclic phase slipping problems. However, they note that differential encoding and decoding introduce an approximately 1 dB penalty in optical signal-to-noise ratio (OSNR) sensitivity, especially when combined with high-coding-gain FEC. To overcome this limitation, the study proposes a training-assisted two-stage phase recovery algorithm, which eliminates the need for differential encoding. This approach reduces the OSNR penalty by about 1 dB and enhances the receiver sensitivity. The work in [16] explores the benefits of a pilot-aided approach to mitigate cycle slips.