capacity region of multiple access channels in VLC networks under both peak and average optical power constraints is investigated in [5]. The authors propose new inner and outer bounds for the channel capacity by developing an innovative approach using an inexact gradient descent method to handle the complex optimization problem. By considering the unique characteristics of VLC, such as non-negative real-valued signals and power constraints, the study demonstrates that the optimal input distributions are discrete and vary depending on the signal-to-noise ratio (SNR). However, VLC is susceptible to interference caused by power attenuation and inherent noise, leading to error propagation. To maintain high-quality telecommunication while controlling costs, the adoption of channel coding is essential. Channel codes are designed to enhance the reliability of data transmission over noisy communication channels by adding redundancy to the transmitted data. This redundancy enables the receiver to detect and, in some cases, correct errors that may occur during transmission. Among the various coding techniques, polar codes are promising [6]. Channel polarization involves combining and splitting channels in a recursive manner, leading to a polarization effect, where the symmetric capacity terms of the resulting channels tend towards 0 or 1. Polar codes, constructed based on this idea, can achieve the symmetric capacity of any given binary-input memoryless channel. In addition, polar codes offer significant advantages, such as low computational complexity, the ease of implementation, and flicker-free operation [7], making them highly suitable for integration into VLC systems. In this study, we propose a novel scheme that incorporates polar codes into VLC channels. The scheme employs a Gaussian approximation to model the polarization behavior within the VLC channel and develops a specialized class of polar codes optimized for VLC. Additionally, a tailored decoding algorithm is designed to accommodate the specific characteristics of the VLC channel. Our experimental results demonstrate that the proposed scheme achieves a minimum coding gain of 5 dB, along with a substantial reduction in bit error rate (BER), significantly improving the reliability of VLC systems. This advancement expands the application of polar codes and enhances the overall performance of VLC technology. The transmission efficiency metric is a crucial metric investigated in the field of telecommunications. VLC, owing to its short wavelength and restricted diffraction, demonstrates susceptibility to obstruction and interference in the transmission link, giving rise to the following scenarios:  
* The transmitter and receiver are not in a direct line-of-sight communication;
* The transmitter and receiver are situated at a considerable distance, making reliable communication challenging. Therefore, implementing a relay scheme is essential to enable bidirectional VLC among multiple users. In traditional relay schemes, relay nodes simply store and forward the data received from source nodes. However, simply routing or replicating at intermediate nodes is generally not optimal. Unlike traditional methods that treat information as a \"fluid\" that can simply be routed or replicated, network coding [8] employs coding strategies at intermediate nodes to optimize information flow. This approach has been shown to be beneficial in saving bandwidth and increasing throughput in multicast scenarios. By allowing nodes to process and combine information in innovative ways, network coding facilitates the more efficient use of network resources [9]. Considering physical-layer network coding (PNC) in a relay-assisted communication system, ref. [10] introduces the PNC concept and its application in improving network throughput. Compared with traditional transmission and straightforward network coding schemes in terms of BER performance, PNC can achieve higher throughput with a slightly worse BER in low-SNR conditions.