## 3 Generalized Color Modulation  
GCM was introduced to make the VLC system color-independent [13; 14]. Using this scheme, it is possible to send any data stream with multiple LEDs that are independent of the target color of the VLC system. Color independency is one of the most important advantages of GCM over other VLC modulation schemes. Because GCM can produce any target color within a gamut area by combining other colors, it is possible to establish accurate communication using a VLC system while maintaining the original color and brightness. The target color can also be demapped on the receiver side from the received color symbols without having information about the target color. Generally, in WDM, transmitter and receiver use a definite number of wavelengths. In contrast, in GCM, the number of wavelengths can be chosen within the visible band depending on the application. In other words, GCM is independent of the number of LEDs and PDs. In addition, a fixed total light intensity can be maintained over time, which allows dimming control and flicker-free operation, whereas other intensity-based modulations (e.g., OOK and PPM) alter the light intensity to send data. To represent the target color, GCM uses a constellation diagram with 2\({}^{\mathrm{m}}\) points (m-bit data) in a color space, with each point in this diagram representing a transmitted data symbol. They are mapped onto RGB LEDs using (4) and (6). On the receiver side, PDs detect the RGB intensities, from which the (x, y) coordinates are determined using (5) and (2). Finally, the error boundary decision (EBD) and the Euclidean distance are used to demap the received points into the original data symbols [15]. Because OFDM is known to be a useful modulation method for VLC systems for several reasons [7; 20; 21], an OFDM-based VLC system that can be color independent using CSBM was presented previously [22]. With all the promising advantages of OFDM, the proposed system can be applied to all colors in the visible band. In a past paper [22], it demonstrated robustness of the  
Figure 2: CIE1931 color space chromaticity diagram [15]. proposed OFDM-VLC system to inter-symbol-interference (ISI) and a large peak-to-average power ratio (PAPR) while maintaining color independency. In GCM, we define the data symbols using a constellation diagram in the color space. We generate the constellation based on two assumptions:  
* The transmitted data symbols are selected in such a way that they are random and equidistant from each other on the circumference of the constellation diagram. * The changing rates of the target color are lower than the data rates. To generate the constellation diagram, we consider two aspects when determining the points in the light color space: (i) colors as symbols are used to determine a target color perceivable to the human eye and (ii) the maximum distance between two adjacent constellation points are preferred in the constellation diagram. In order to reduce the symbol error rate (SER), the first assumption is the best choice because it minimizes the effect of interference. Additionally, the area of the constellation diagram has to be maximized when the second aspect is considered. The area of constellation diagram is maximized in two ways: (i) the coordinate of the target color becomes the center of constellation diagram and (ii) the coordinates of the LEDs are used to form the gamut area. Based on this, the maximum area of a constellation diagram is constructed by drawing the largest circle inside the gamut area in a manner so that the center of the largest circle represents the target color point. Figure 3 represents the generation of a constellation diagram with a target color [14]. In this case, the constellation points are arranged using a similar arrangement to that of RF circular quadrature amplitude modulation (QAM). More examples of circle-type and line-type constellation diagrams can be found in a past paper [16]. We suppose that equiprobable symbol transmission is valid due to the compensation and interleaving algorithm.