## 1 Introduction  
Due to the great demand for higher data rate transmission and the over-crowdedness of the bandwidth of conventional radio frequency (RF) based communication technology, the use of visible light communication (VLC) as an alternative technology has aroused considerable interest from researchers. With the wide unlicensed spectrum, VLC has the potential to transmit high-speed data without electromagnetic interference [1; 2; 3; 4]. Combining illumination and communication, VLC has many application scenarios, such as indoor positioning, underwater communication, and intelligent vehicles system. Light-emitting diodes (LED) and laser diodes (LD) are two kinds of transmitters in a VLC system. In a previous report, with a single-color LED, more than a 3 Gbps data rate was successfully achieved [5] and more than a 20 Gbps VLC system based on a multichromatic LED array chip was experimentally demonstrated utilizing wavelength-division-multiplexed technology [6]. Micro-LED was able to accomplish around a 10 Gbps data transmission rate based on a higher bandwidth [7]. However, due to the limited modulation bandwidth of LEDs at 10 s-100 s MHz and the efficiency droop problem for micro-LED [8], realizing a much higher data rate (gigabit class range) is still a challenge.  
In contrast to LED, LD has a much higher modulation bandwidth and the highest electrical-to-optical conversion efficiency [9]. What's more, LD owns the advantages including light beam convergence and high optical power. Therefore, LD may be a better candidate for front-end transmitters in a VLC system to realize a high Gbps data rate. In [10], [PERSON] et al. realized a data rate of around 6 Gbps by utilizing orthogonal frequency-division multiplexing (OFDM) with a fixed-rate and bit loading scheme. [PERSON]'s group demonstrated 9 Gbps error-free data transmission in a 450-nm GaN LD-based VLC system with the bandwidth of 1.5 GHz [11] and they further extended the bandwidth to 3.2 GHz through an impedance matched hardware circuit, achieving a data rate of 14 Gbps [12]. A higher data rate of 15 Gbps was accomplished by [PERSON] et al., with adaptive bit loading extending the effective bandwidth to 2.5 GHz [13], and a 16.6 Gbps data transmission was realized in [14] by using bit-power loading and post equalization. LD emerges to be a promising light source for high-speed VLC applications [15].  
The aforementioned work done on LD utilized bit loading or bit and power loading to improve system performance. By reallocating the available power and distributing the total number of bits over subcarriers, bit and power loading helps to raise the spectral efficiency [16]. However, the allocated bit can only be an integer and there still exists a capacity gap to the Shannon limit. As an emerging cutting-edge constellation shaping scheme, probabilistic shaping (PS) can provide additional shaping gain by changing the probability of each constellation point to make a Gaussian-like constellation [17; 18]. PS can be combined with bit loading to further eliminate the gap to the Shannon capacity.  
In this paper, for the first time, PS bit loading discrete multi-tone (DMT) modulation is investigated in a high data rate VLC system based on a 450-nm GaN LD. Utilizing the proposed entropy-loading strategy, higher entropy can be achieved compared to bit and power loading. The characteristic of the system is also discussed in detail. With PS bit loading, an achievable information rate (AIR) of 10.23 Gbps was achieved over 1.2 m in free space. The normalized generalized mutual information (NGMI) among all subcarriers were above 0.92, showing that there exist margins in the system. Experimental results show the potential of PS bit loading to increase the system capacity.  
The following sections are organized as follows: the principle of PS bit loading is introduced in Section 2. Section 3 shows the experimental setup of the system. The system performance will be discussed in Section 4. In Section 5, we will draw the conclusion.