## 1 Introduction  
The never-ending demands for higher data rates always exist in a variety of industry fields, which require significant efforts to satisfy the growing data demands and to deal with the incoming bandwidth capacity crunch [1, 2, 3], pushing researchers to pay more attention to spectrally efficient modulation formats [4]. For high data-rate transmission, the coherent communication has already become the standard communication technique in metro and long-haul networks and is becoming more and more widely applied into the datacenter space. The coherent optics has been used as a key technology for 400 G and higher data rate transmission [5]. Quadrature amplitude modulation (QAM) formats have been investigated in [6, 7] to have an excellent performance in achieving higher spectral efficiency with the same forward error correction (FEC) overhead [8]. Compared with the widely used QAM modulation formats in coherent optical communications, the more complex modulation formats, such as 4-dimensional signaling [9, 10, 11, 12], can offer us better power efficiency, by increasing the Euclidean distance between constellation points for a given signal power when compared to the 2D signal space. The 4D modulation formats applications are investigated mainly for long-haul transmission [13], but have also been demonstrated to have advantages for metro networks applications in our previous work [10]. DWDM is an efficient way to increase overall capacity by allocating a huge amount of data to different wavelength channels and transmit them simultaneously [14, 15, 16, 17, 18, 19]. The application of pulse shaping scheme, together with the DWDM system, can offer us better spectral efficiency [19]. FEC coding is an efficient method to increase the channel performance. Researchers have investigated the bit error rate (BER) performance with different codes [20; 21] and found the low-density parity-check (LDPC) coding outperforms other coding schemes in the high code rate region. The capacity of DWDM optical transmission system can be increased significantly with the application of digital signal processing (DSP). To enable advanced modulation formats, the requirement of better DSP is also increasing rapidly [22]. The phase recovery algorithms for the complicated modulation formats are already investigated in [23; 24], but more complicated DSPs bring us extra costs, and the conventional DSP-based receivers require high-power consumption. While the demands of different modulation formats applications are increasing, a DSP application-specific integrated circuit (ASIC) is also required to support multi-modulation and multi-rate formats [25]. Researchers have already investigated DSP-ASIC to support QAM modulation formats with different constellation points for different data rate transmissions [25; 26; 27]. The constellation shaping scheme, both probabilistic shaping (PS) and geometric shaping (GS), are broadly applied to reduce the gap of channel capacity to Shannon limit, which also require specified DSP scheme to optimize the performance [28; 29]. These increasing demands of DSP costs have led researchers to pay more attention to the DSP-free coherent receivers [30; 31; 32; 33]. On the other hand, the terabit optical Ethernet technologies will be affected by security issues, and to solve such problem, the properly designed fiber Bragg gratings (FBGs) application in impulse responses derived from mutually orthogonal Slepian sequences has been advocated in [1] to enable positive rate to convert optical communications [2; 3]. In this invited paper, we apply the Slepian sequences-based basis functions to a 16-points 4D modulation format, combined with the LDPC coding for 40 km metro network transmission. We find that with the application of Slepian sequences, the 4D modulation format can be implemented using an I/Q modulator and recovered on receiver side without any high power demanded DSP. The LDPC coding works properly with such a new modulation scheme.