## 5 Deep Learning Approach for Possible VLC System Enhancement
### Bidirectional LSTM Approach for the Distortion Correction  
Unlike the classification and detection based on image processing, sequential data such as voice samples or text sentences correlate between present and past times. A Recurrent Neural Network (RNN) is the prime example of processing input data with network weights and structure. It also preserves the sequences of the data with the network hidden states. However, RNN has severe issues with vanishing and exploding gradient programs for the training and optimization process, resulting in the incapability of learning long-term knowledge. Long Short-Term Memory (LSTM) is one of the main algorithms to resolve these issues with RNN. LSTM contains multiple activation function modules called gates to overcome the gradient matters. This LSTM system contains memory that takes previous and current states as input, as shown in Figure 5.  
Each element in the LSTM unit, so-called a gate, leads the LSTM unit to store and discard the data information. Apart from input and output gates, the forget gate is another key LSTM feature that controls knowledge preservation in LSTM units. Details of each parameter in Figure 5 are below [13; 14]. Note that \(\sigma\) and \(\tanh\) are defined as the sigmoid function and the hyperbolic tangent activation function. \[i_{t}= \sigma(W_{i}x_{t}+U_{i}h_{t-1}+b_{i}) \tag{8}\] \[f_{t}= \sigma(W_{f}x_{t}+U_{f}h_{t-1}+b_{f})\] (9) \[C_{t}= f_{t}C_{t-1}+i_{t}\tilde{C}_{t}\] (10) \[= f_{t}C_{t-1}+i_{t}\tanh(W_{c}x_{t}+U_{c}h_{t-1}+b_{c})\] (11) \[O_{t}= \sigma(W_{o}x_{t}+U_{o}h_{t-1}+b_{o})\] (12) \[h_{t}= O_{t}\tanh(C_{t}) \tag{13}\]  
Note that \(i_{t}\), \(f_{t}\), \(C_{t}\), \(O_{t}\), and \(h_{t}\) are the input gate, forget gate, memory cell, output gate, and hidden state at time step \(t\), respectively. In addition, \(W_{i}\), \(W_{f}\), \(W_{o}\), and \(W_{c}\) are the input weight matrices of parameters \(i\), \(f\), \(O\), and \(\tilde{C}\), and \(U_{i}\), \(U_{f}\), \(U_{o}\), and \(U_{c}\) are the hidden layer weight matrices of parameters \(i\), \(f\), \(O\), and \(\tilde{C}\). In each formula, \(b_{i}\), \(b_{f}\), \(b_{o}\), and \(b_{c}\) are the biased parameters for \(i\), \(f\), \(O\), and \(\tilde{C}\). Once the LSTM unit took previous memory cells and  
Figure 5: A basic diagram of the LSTM unit. Note that it is known to be the general structure of modern LSTM unit, and the similar and identical LSTM units are referred to in various literature [13; 14; 15; 16]. hidden states from the previous LSTM units as \(C_{t-1}\) and \(h_{t-1}\), it processed the following sequential input at times \(t\) and \(x_{t}\) to produce the present memory cell and hidden state, \(C_{t}\) and \(h_{t}\). As illustrated in this general structure of the LSTM unit, the data sequence is a forward sequence. However, the data sequence information in forward and backward sequences can be different, and understanding the backward data sequence can produce the data prediction well. These are the main reasons why Bidirectional LSTM should be considered. A brief block diagram of the BLSTM structure is shown in Figure 6. In this figure, the BLSTM first processes the forward LSTM before processing the backward LSTM, and the activation function produces the result [15]. Hence, this system contains the past and future input data. BLSTM is a significant advancement of LSTM schemes that train the neural networks with the forward and backward data sequences [17]. Eventually, it aims to train with the data sequences to correct or predict future data. Existing example applications include speech recognition and stock index prediction [18]. Since our VLC systems process continuous time-domain signal data, LSTM becomes a suitable option for distortion correction. However, traditional LSTM trained in the forward direction of the data or signal sequence can become biased for signal correction. On the other hand, Bidirectional LSTM processes the backward and forward of the signal sequences to train both sequence directions of the signal.