## 3 System Description
In hierarchical 16 QAM, the first and third bits represent HP bits, while the second and fourth bits represent LP bits. Generally, increasing the value of \(\alpha\) enhances the protection of the important codeword \(c1\) but weakens the less important codeword \(c12\), and vice versa. Figure 2: Hierarchical 16 QAM constellations: Black points represent virtual symbols, enhancing error protection for critical data, while white points indicate actual transmitted symbols. This means that a high value of \(\alpha\) does not guarantee high quality because the degradation of \(c_{12}\) affects both the RGB and depth videos. Therefore, finding a suitable value of \(\alpha\) is crucial for improving the quality of the stereoscopic 3D video. The detailed formulation for determining the optimal value of \(\alpha\) is discussed later. The process for generating the symbol \(x_{B}\) at node B is identical to the process for \(x_{A}\), and thus, it is omitted for brevity. The transmitted symbols \(x_{A}\) and \(x_{B}\) are directly exchanged between nodes A and B during the first and second time slots and are also received at the relay node R due to the wireless broadcast nature of the transmission. At the relay node, the received symbols are demodulated and decoded into bitstreams \(\tilde{u}_{1}\) through \(\tilde{u}_{4}\). These decoded bitstreams are then re-encoded using network and channel coding methods. This paper explores three such methods, as illustrated in Figure 3. Figure 3a shows the proposed method, while Figure 3b,c depict the first and second reference methods, respectively. In the proposed method shown in Figure 3a, the decoded bitstreams containing 2D color videos (\(\tilde{u}_{1}\) and \(\tilde{u}_{3}\)) and the corresponding depth maps (\(\tilde{u}_{2}\) and \(\tilde{u}_{4}\)) are first combined into \(\tilde{u}_{13}\) and \(\tilde{u}_{24}\), respectively, using an XOR operation. These combined streams are then separately encoded using a 1/2 RSC encoder. Following this, \(\tilde{u}_{13}\) is interleaved and combined with \(\tilde{u}_{24}\) to form \(\tilde{u}_{1234}\), and the parity bitstreams \(\tilde{p}_{13}\) and \(\tilde{p}_{24}\) are punctured using an odd-even puncturing technique. As a result, the length of the concatenated codeword stream \(\tilde{c}_{1234}\) is halved, allowing it to be modulated using low-order modulation schemes such as 4 QAM or QPSK. In the first reference method (reference 1) shown in Figure 3b, the process begins similarly to the proposed method, with the decoded bitstreams containing 2D color videos (\(\tilde{u}_{1}\) and \(\tilde{u}_{3}\)) and the corresponding depth maps (\(\tilde{u}_{2}\) and \(\tilde{u}_{4}\)) are combined into \(\tilde{u}_{13}\) and \(\tilde{u}_{24}\), respectively, using an XOR operation. The channel coding then follows the same process as the existing IL-FEC method used at nodes A and B. Consequently, the length of the relayed codeword stream \(\tilde{c}_{1234}\) is identical to that of the transmitted codeword streams from nodes A and B, and this stream is modulated using hierarchical 16 QAM. This approach has been proposed in previous studies [6; 11] In the second reference method (Reference 2) shown in Figure 3c, the XOR-based network encoding and channel coding using 1/2 RSC encoders follow the same procedure as in the first reference method shown in Figure 3. However, in this method, only the parity streams \(\tilde{p}_{13}\) and \(\tilde{p}_{24}\) are modulated using QPSK, without the source streams. This approach of retransmitting only parity bitstreams has been proposed in previous studies [14; 15]. In the third time slot, nodes A and B demodulate the directly received symbols \(y_{BA}\) and \(x_{AB}\), as well as the relayed symbols \(y_{RA}\) and \(y_{RB}\), respectively. For this demodulation, each node utilizes a soft-bit demodulator, which is detailed in the appendix.