## 1 Introduction  
Visible light communication (VLC) has recently become popular as an alternative to radio and infrared communication systems [1; 2; 3]. Visible light has several features that distinguish it from radio frequencies, such as the availability of unique bandwidths that are not subject to interference from electromagnetic waves. At the same time, light-emitting diodes (LEDs) offer benefits over other light sources, such as high speed, small size, long lifetime, and rapid switching. By combining these two factors, it is possible to provide high-speed communication using VLC while maintaining the basic functionality (e.g., illumination, displays, etc.) of visible light. Compared to radio frequency (RF) communication systems, VLC systems offer distinct channel characteristics and signal sources. Variable on-off keying (VOOK), variable pulse position modulation (VPPM), multiple PPM (MPPM), pulse dual slope modulation (PDSM), orthogonal frequency division multiplexing (OFDM), and subcarrier modulations are well-known modulation schemes of VLC systems [4; 5; 6; 7; 8]. Note that intensity variation of the optical signal is the main key point of these modulation schemes. In wavelength division multiplexing (WDM), different wavelengths are used to multiplex various optical signals into a single optical fiber [9]. WDM can be used in VLC systems by implementing it with LEDs of different wavelengths by varying the intensity of the signals to transmit information data. To receive the transmitted data, a photodiode (PD) along with different band-pass filters are used. Finally, the transmitted data is recovered by demodulating the received signal on PD. Color-shift keying (CSK), the first color space-based modulation scheme, was proposed by the IEEE 802.15.7 Task Group [10; 11]. However, CSK is not suitable for communication under target color variation and, in which case, CSK may exhibit lower performance than traditional intensity-based WDM [10]. The target color indicates the desired color for LED lighting. In a past paper [12], constellation designs for CSK were examined using billiard algorithms, however, any analytical verification could not be shown for the solution of constellation design for balancing color. In numerous instances of the literature [13; 14; 15; 16], to overcome this limitation, generalized color modulation (GCM), one of the color-space-based modulation (CSBM) methods, was introduced and resolved for the color-independent VLC systems. The term \"color-independent\" implies the independence of light color and intensity variations. In this way, a VLC system can perform seamless communication that can preserve the originality and brightness of lighting color. In other words, GCM allows communication without compromising the original lighting color. As a result, any data stream can be delivered using GCM regardless of the target color. GCM also has a number of other advantageous features, such as dimming control, color independence, independence from the number of LEDs and PDs, and acceptable BER performance in the presence of color variation. Figure 1 presents a simple conceptual block diagram of a color-space-based VLC system in comparison to a carrier-signal-based RF system. However, previous studies in wireless optical communication using visible light with photodiode receivers have either been limited to short distances or have required complicated processing at the receiver. Photodiodes can convert pulses at a fairly high rate but suffer from significant interference and background light noise. As a result, the signal-to-noise ratio (SNR) is very low and the communication range shortened. It is possible to overcome this data transmission rate limit  
Figure 1: Color-space-based visible light communication (VLC) system vs. carrier signal-based RF system. (**a**) RF communication with carrier-based constellation; (**b**) VLC with color-space-based constellation.