## 7 Conclusions  
In our paper, we observed the nonlinearity of LEDs, and it could significantly affect the performance of optical OFDM transceiver systems. The compensated module using predistortion can substantially enhance the OFDM system performance for performance improvement. However, the existing compensation methods directly have to measure LED nonlinearity or high complex characteristics. In the OFDM-based VLC system, we proposed the practical predistortion scheme with coefficient approximation. The coefficient approximation showed the effectiveness of simple operations without a necessary sampling of the LED transfer function by using the inverse function. By simply tuning the coefficient, the OFDM system showed outperformed results compared to the system without the predistortion.  
In addition, we proposed a Bidirectional LSTM model to handle the variation and distortion of LEDs without distortion modeling. We used the distortion data from our distortion models for the training purpose, and the results showed the possible promise of performance improvement. Possible discussion associated with BLSTM approaches is as follows.  
* We used the simple BLSTM structure and improved distortion. However, our BLSTM structure did not address the phase issues. Since the BLSTM model cannot handle complex number data, we separated real and imaginary data and produced two models. No consensus existed between the two trained models. A significant performance improvement could be possible if we designed the BLSTM model with an interconnected structure.
* We considered the white LED case only in this experiment. To process red and infrared LEDs, BLSTM models have to be retrained. Even if we retrained the model, it is not guaranteed whether or not those models can produce the equivalent performance on those diodes. Diode-specific model structure must be explored.
* Assuming we have no prior knowledge of LEDs, the distortion correction with one model would simplify the system structure and reduce its complexity. To handle all LED distortion into one model, we may need to design a deep learning structure more complex than our tested BLSTM model.
* For our BLSTM model training, computing power is the primary factor in our proposed VLC scheme, and our initial studies encountered the limitation of the computing resources. Our future works must extend to various BLSTM layer lengths and structures, assuming we have considerable computer powers. When the VLC scheme becomes part of the 5G NR light radio family, possible opportunities for our BLSTM model are available to be trained into the cloud or multi-access edge computing (MEC) on a large scale.  
In addition to our work, it would be possible to extend our BLSTM approach to the practical and effective implementation of the predistortion module and explore other deep learning models and structures dedicated to the hardware module in VLC systems for possible future work.  
Conceptualization, [PERSON]-J.P. and [PERSON]-Y.K.; methodology, [PERSON]-J.P. and [PERSON]-Y.K.; software, [PERSON]-J.P. and [PERSON]-Y.K.; validation, [PERSON]-J.P. and [PERSON]-Y.K.; investigation, [PERSON]-J.P., [PERSON]-Y.K. and [PERSON]-I.J.; resources, [PERSON]-J.P. and [PERSON]-I.J.; data curation, [PERSON]-J.P. and [PERSON]-Y.K.; writing, [PERSON]-[PERSON], [PERSON] and [PERSON]; visualization, [PERSON] and [PERSON]; supervision, [PERSON], [PERSON] and [PERSON]; project administration, [PERSON], [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Sungshin Women's University Research Grant of 2021 and the Technology Innovation Program (20013726, Development of Industrial Intelligent Technology for Manufacturing, Process, and Logistics) funded by the Ministry of Trade, Industry and Energy (MOTIE, Korea).  
The authors declare no conflict of interest.