## 3 System Description  
We focus on TWRC systems specifically designed for the transmission of 3D video in the MVD format. In this format, nodes A and B communicate via a relay node, R, utilizing network coding based on the Log-likelihood Ratio (LLR). Each node operates under a time-division half-duplex mode, meaning that they cannot transmit and receive simultaneously. Therefore, the proposed system requires three distinct time slots to complete the communication process. As illustrated in Figure 1, nodes A and B exchange 3D video content formatted in the MVD format, which includes both multi-view video and corresponding depth maps. At node A, the multi-view RGB video and depth information are separately compressed into bitstreams \(u_{1}\) and \(u_{2}\), respectively, using multi-view video coding (MVC) [16]. To enhance transmission reliability, we apply the IL-FEC scheme as the channel coding method. In this process, the bitstream \(u_{1}\), which contains the critical 2D color video data, is first interleaved and then combined with the depth map bitstream \(u_{2}\) (i.e., \(\prod(u_{1})\oplus u_{2}=u_{12}\)), where \(\prod(\cdot)\) represents the Universal Mobile Telecommunication System (UMTS) interleaver, and \(\oplus\) denotes the XOR (exclusive OR) operation. The primary purpose of combining these streams (i.e., the XOR operation) is to introduce redundancy, ensuring the important 2D color video data are more robust against errors, interleaving further dispersed errors, and improving overall transmission reliability. Following this, the crucial bitstream \(u_{1}\) and the combined bitstream \(u_{12}\) are encoded into codewords \(c_{1}\) and \(c_{12}\), respectively, using two Rate-1/2 Recursive Systematic Convolutional (RSC) encoders. These codeword streams are then mapped to different priority levels for modulation: \(c_{1}\) to high-priority (HP) bits and \(c_{12}\) to low-priority (LP) bits. Our approach leverages Hierarchical Quadrature Amplitude Modulation (HQAM) to prioritize the transmission of different data layers--assigning higher protection to the more critical color data (\(c_{1}\)) while allowing the depth data (\(c_{12}\)) to receive weaker protection, which is  
Figure 1: The proposed system model. suitable for its role in depth rendering. This differentiation is crucial for maintaining the perceived quality of 3D video content, as even minor degradation in color data can significantly affect user experience, whereas the impact of errors in depth data is comparatively less perceptible. This hierarchical approach is specifically tailored to 3D video. Figure 2 presents the constellation diagram for hierarchical 16 QAM modulation. In this diagram, black points indicate virtual symbols, while white points represent the actual transmitted symbol \(x_{A}\). The symbol \(x_{A}\) can be expressed mathematically as:  
\[x_{A}=K\Big{\{}f^{16}_{(\alpha)}\Big{(}c^{(2m-1)}_{1},\,c^{(2m-1)}_{12},c^{2m} _{12},\,c^{2m}_{12}\Big{)}\Big{\}} \tag{1}\]  
where \(1\leq m\leq M\), and \(m\) represents the \(m\)-th bit constituting the transmitted symbol \(x_{A}\). The function \(f^{16}_{(\alpha)}(\cdot)\) represents the hierarchical 16 QAM mapper, where \(\alpha\) is a hierarchical value that determines the balance of protection between critical and non-critical data by adjusting the distances between constellation points. The hierarchical value \(\alpha=d^{\prime}_{1}/d_{2}\), where \(d^{\prime}_{1}\) is the minimum distance between two actual (white) symbols in adjacent quadrants. It is crucial to note that \(d^{\prime}_{1}\) is related to \(d_{1}\) and \(d_{2}\) through the equation \(d^{\prime}_{1}=d_{1}-d_{2}\)[17]. Here, \(2d_{1}\) represents the distance between the virtual center points of the quadrants, and \(2d_{2}\) represents the distance between the actual transmitted symbols within each quadrant. Additionally, \(K\) serves as a scaling factor to normalize the average symbol energy to unity, as detailed in [13].