## 1 Introduction  
Visible light communication (VLC) is a promising technique for indoor short-range wireless communications systems [1, 2]. It has many advantages such as high anti-electromagnetic interference, low cost, good safety, and a rich and license-free spectrum. Compared with the single carrier modulation schemes, the optical orthogonal frequency division multiplexing (O-OFDM), which has a higher spectral efficiency and system capacity, attracted more and more attention from scholars [3, 4, 5]. Combining the low-cost structure of intensity modulation and direct detection (IM/DD), the direct current-biased (DC) O-OFDM has been widely deployed in the VLC system to achieve a high-speed rate [6], where the Hermitian symmetry is adopted to provide the real-valued signal and the DC bias is used to ensure the non-negativity constraint of light-emitting diode (LED). However, the modulated signal always suffers from the inherent VLC channel impairments, involving the LED nonlinearity and the optical diffuse propagation. Especially for the case of the signal with a large bandwidth and a high output power, the overall channel impairment is detrimental and will damage the system performance severely, which imposes a big challenge to existing transceiver designs [7]. In general, the nonlinear effect of the LED and the dispersive effect of the optical multipath channel can be handled independently or jointly. Various schemes have been investigated to overcome the channel impairments in VLC systems, such as the peak to average power ratio (PAPR) reduction associated with the OFDM system [8; 9; 10; 11; 12], predistortion technique [13; 14], nonlinear post-equalizer (NPE) scheme [15; 16; 17; 18], and bit-interleaved coding [19], etc. Although the PAPR is easily implemented at the transmitter, the memory effect of LED is neglected, which degrades the system performance in high-speed transmission [11; 12]. The predistortion technique is an efficient way to mitigate the LED nonlinearity; however, the dispersive effect of the multipath VLC channel is not taken in account [13; 14]. Thus, the specified equalizer should be employed at the receiver to maintain the overall performance, which inevitably increases the system cost. Unlike the predistortion at the front end, the NPE at the receiver end is cost-efficient and seems more competitive because it can mitigate the overall impairment from the cascade of the LED and the dispersive optical channel. At present, there are many methods to construct the NPE. As for polynomial model approaches, a complex mathematical expression must be always built first and employed as an equalizer model, which have a great effect on the modeling accuracy. As in the strong nonlinear and complex multipath scenario, the model coefficient identification is usually intractable for some conventional signal processing methods, which come across the computational complexity and storage problem. Moreover, machine learning (ML)-related algorithms have also demonstrated the ability to solve the nonlinear issues [20; 21; 22; 23], e.g., support vector machine (SVM) and K-means algorithm, can be adopted to estimate various channel impairments and to accurately identify the complex mapping relationship between the input and output signals. Deep learning (DL) has regained traction tremendously in recent years. Due to its strong ability to learn, recognize, and predict, DL has been regarded as a promising tool in solving the complex communication problems in unknown or complex channels. A comprehensive introduction and overview of the application of DL in wireless communications has been reported in [24; 25; 26; 27; 28; 29; 30; 31; 32; 33], including the fully connected deep neural network (FC-DNN)-based channel estimation, nonlinearity compensation, signal detection, and decoding scheme. In addition, DL has also been applied in VLC to enhance the system performance.