## 2 Augmentation of Li-Fi Wireless DMT Transmission Capacity Through Sparse Coded Mask Optimization  
### Sparse Coded Mask Modeling for DMT Signal  
As mentioned in the introduction, the DMT signal can be considered a type of MTSD. The reasons for this are as follows: First, each subcarrier in the DMT signal can be viewed as a modulated signal over time, and thus can be recognized as a function of time. In this respect, it is very similar to time-series data. Second, if the DMT signal is analyzed in the time domain for each subcarrier, each subcarrier signal can be considered a separate time-series dataset. In this case, these individual time-series datasets coexist simultaneously and interact with each other (by maintaining orthogonality between subcarriers). Therefore, the entire set of the DMT signal can be viewed as MTSD. Based on the results of the existing studies [15; 16; 17; 18], we anticipate that it should be possible to mask (delete) and then recover DMT signals, which exhibit characteristics that are very similar to MTSD. Figure 1 shows the process of increasing the transmission capacity of DMT signals during optical wireless transmission using the proposed sparse coded mask modeling technique. A DMT signal, \(X\), with \(N\) subcarriers, which is encoded by quadrature phase shift keying (QPSK) symbols, is fed into a masked autoencoder and then divided into \(k\) segments. These \(k\) segments are transformed into DMT patches through a one-dimensional convolution operation. Afterward, a positional encoding process is applied, adding one positional encoding (marked in black in Figure 1) to the \(k\) DMT patches. Out of the \(k\) DMT patches, only \(d\) (where \(d\ll k\)) patches are randomly retained, while the \(k-d\) remaining patches are masked (deleted). Finally, the latent representation of the DMT signal, which fully reflects the original characteristics of the DMT signal, is then obtained as the output signal of the encoder. Therefore, since the length of the encoded DMT signal (the latent representation of the DMT signal) after masking is reduced compared to the original DMT signal, the length of the encoded optical DMT signal, after being directly modulated by the white LED and then transmitted, is also reduced. This means that, from the perspective of a typical data transmission system, the DMT signal is transmitted in a compressed form. After optical wireless transmission, the encoded DMT signal, which is received at the photo-detector, is recovered to the original DMT signal through a decoding process. Therefore, by compressing the length of the original DMT signal during optical wireless transmission, the channel capacity within one second is increased. First, the process by which the length of the QPSK-encoded DMT signal is reduced (compressed) using the proposed MAE-based sparse coded mask modeling technique can be mathematically described as follows. The DMT signal, \(U(m)\), corresponding to one symbol in Figure 1, can be expressed as Equation (1):  
\[U(m)=\frac{1}{\sqrt{2N}}{\sum_{n=0}^{2N-1}}\ C_{n}\ \exp\ (j2\pi n\frac{m}{2N}),\ m=0,1, \ldots,2N-1 \tag{1}\]  
where \(U(m)\) is a sequence of real-valued numbers composed of \(2N\) points, which is the result of applying the IFFT (Inverse Fast Fourier Transform) to all \(2N\) points. \(N\) is the number of subcarriers. \(C_{n}=A_{n}+jB_{n}\) is the complex values according to QPSK modulation. \(A_{n}\) is the in-phase component and \(B_{n}\) is the quadrature component. Next, a CP (Cyclic Prefix) of length, \(N_{cp}\) was added to the DMT signal, \(U(m)\), in order to maintain orthogonality, as shown in Equation (2). \[X(m)=\frac{1}{\sqrt{2N}}{\sum_{n=0}^{2N-1}C_{n}}\exp\left[j\frac{2\pi n\big{(}m- N_{cp}\big{)}}{2N}\right],\ m=0,1,\ldots,2N+N_{cp}-1 \tag{2}\]  
where \(X(m)\) is the DMT signal with CP. After the parallel to serial conversion, its total length becomes \(\big{(}2N+N_{cp}\big{)}\). This is fed into the MAE. The MAE process consists of two stages.