## 2 Augmentation of Li-Fi Wireless DMT Transmission Capacity Through Sparse Coded Mask Optimization
### Sparse Coded Mask Modeling for DMT Signal
The encoding is structured as follows: The even dimensions (\(m=2j\)) use the sine function, which increases gradually over time. The odd dimensions (\(m=2j+1\)) use the cosine function, which is phase-shifted by \(\frac{\pi}{2}\), providing an alternating representation. This alternating pattern ensures that the encoding remains linearly separable, meaning that the model can compute meaningful distances between different positions in the sequence. In the random masking process, \(d\) patches are randomly selected (\(d\ll S\)) out of the \(S\) patches. The remaining patches (\(S-d\)) are all masked, or in other words, deleted. Eventually, the remaining patches adding the positional encoding patch, \(E_{position}\), become the latent representation of DMT signal. In this way, the length of the transmitted DMT signal can be reduced. From the perspective of a typical data transmission system, this can be referred to as compression. The set of randomly selected patches with \(d\) elements, \(P_{patch}\), can be expressed as shown in Equation (6). \[P_{patch}(=\{P_{1},P_{2},\ldots,P_{m},\ldots,P_{S}\})\subset P_{i}(m)\Big{(}= \sum\
olimits_{k=0}^{K-1}h_{k}\cdot x_{i}(m-k)\Big{)} \tag{6}\]  
At the receiver-side, including the photo-detector with decoder, as depicted in the right box of Figure 1, the primary task is to reconstruct the deleted DMT patches that were masked at the transmitter-side including white LED with masked auto-encoder. The reconstruction is performed using a masked autoencoder (MAE)-based deep learning model, which learns to infer the missing DMT patches based on the transmitted ones. The overall receiver-side process can be divided into the following steps. The optically modulated signal is received by a photo-detector (PD) and then the detected electrical signal is amplified and converted back into digital form via an analog-to-digital converter (ADC). Next, the received signal is divided into DMT patches, just like at the transmitter. The positions of the deleted patches are determined using positional encoding, ensuring that the decoder can infer the correct locations. Next, the received DMT patches (both unmasked and masked ones) are input into a deep learning decoder that reconstructs the missing patches. The model learns to predict the missing patches using adjacent patch information. As shown in Equation (7), the reconstruction function can be represented as follows:  
\[\hat{P}_{m}=f_{decoder}(P_{1},P_{2},\ldots,P_{m},\ldots,P_{S}) \tag{7}\]  
where \(\hat{P}_{m}\) is the reconstructed DMT patch, \(P_{i}\) are the available (unmasked) patches, and \(f_{decoder}\) is the neural network used for reconstruction. Next, the reconstructed DMT signal is reassembled by combining both original and reconstructed patches. The signal is then converted from parallel to serial and undergoes an inverse discrete Fourier transform (IDFT). After reconstructing the complete DMT signal, the cyclic prefix (CP) is removed. The demodulation process extracts the QPSK symbols using discrete Fourier transform (DFT). We proposed a masked autoencoder (MAE)-based sparse coded mask modeling technique, which is a self-supervised learning approach. The model follows an encoder-decoder architecture, where the encoder compresses the unmasked patches into a latent representation, and the decoder reconstructs the missing patches. The encoder only receives a subset of the original patches (i.e., the unmasked patches). These patches are embedded into a high-dimensional space using a 1-D convolutional embedding layer. The encoded representation is then fed into a transformer-based neural network to learn contextual relationships between patches. On the other hand, the decoder takes both the encoded patches and positional encoding information. A self-attention mechanism is applied to infer missing patches based on adjacent ones. The final output is a reconstructed version of the complete DMT signal, including the originally missing patches.