## 1 Introduction  
Recent rapidly grown data traffic in the information and communication networks require high capacity short-reach (<100 cm) interconnected technology inside information and communications technology (ICT) equipment such as servers, routers, and storage [1]. On the other hand, the continuous growth of computing power is a leading cause of improvements to server performance and is also responsible for expanding server consolidation by virtualization. Such consideration requires a high bandwidth data communication intra blade server, which is an aggregate of compact servers connected via the backplane whose data connection capacity depends on the backplane performance [2]. Optical interconnect technology is an attractive candidate for enlarging data connection capacity due to this technology's high-speed transmission and low interference between signals [3]. Optical interconnect technology enables the use of a higher bandwidth backplane compared with electrical interconnection. At present, the standardization of the single-wavelength 100 Gb/s transmission systems is under considerations by Institute of Electrical and Electronics Engineers (IEEE) and Multi Source Agreement (MSA). It is of great significance to realize the transmission rate of over 100 G in backplane interconnection [4]. Recently, optical backplanes based on board-level optical polymer waveguides have attracted increasing attention in the field of optical interconnects, mainly because optical backplanes can become a key enabler for electro-optic integration, which allows for the seamless mating of numerous optical interfaces. Besides that, optical backplanes help to avoid cumbersome cable handling at a board level [5]. According to the development trend of optical interconnect technology predicted by International Business Machines Corporation (IBM) statistics, optical interconnect technology has entered the stage of the optical interconnection between sub-boards and boards [6]. Hence, optical backplane interconnection technology has emerged to prepare an optical waveguide layer on a standard printed circuit board (PCB) or to embed the optical waveguide as a sandwich in the PCB, thereby realizing optical signal interconnection. A large optical backplane with embedded graded-index glass waveguides and fiber-flex termination was studied in [7]. [PERSON] proposed a hybrid bidirectional optical backplane with multiple bus lines [8]. A glass-based 40 cm optical backplane with 0.1 dB/cm insertion loss was fabricated by our group [9]. In order to achieve a high rate and maintain a low cost, it is expected that low-cost bandwidth level optoelectronic devices will still preferred to be used in optical backplane interconnection systems [10; 11; 12; 13; 14; 15; 16; 17; 18], so high spectrum efficiency modulation formats such as four level pulse amplitude modulation (PAM-4) and duobinary are being considered for introduction. Meanwhile, considering its high insertion loss and strong modal noise, the optical backplane transmission system can be regarded as a bandwidth-constrained system with a high insertion loss, so strong equalization algorithms are then required. Transmission at bit rates up to 50 Gb/s over 200 m of multimode fiber (MMF) assisted by decision feedback equalization (DFE) was demonstrated in [18]. The 850 nm laser-based transmissions of 112 Gb/s PAM-4 over 100 m optical multi-mode 4 (OM4 ) MMF assisted by maximum likelihood sequence estimation (MLSE) was experimentally demonstrated in [19]. Moreover, a 135 Gb/s discrete multitone (DMT) transmission using pre-distortion was realized in [20]. Pulse shaping was applied in [21; 22] to achieve error-free 100 Gb/s PAM-4 transmission over a 100 m wideband fiber. However, all the receiving sensitivities of the above schemes were no less than \(-4\) dBm at 100 Gb/s under the 7% hard-decision forward error correction (HD-FEC) threshold. Machine learning has become popular and has attracted increasing attention from optical communities.