# Resource Optimization for 3D Video SoftCast with Joint Texture/Depth Power Allocation
## 2 Related Work
### SoftCast Power Allocation  
In a conventional wireless video transmission scheme, the real-value coefficients are transformed into a bitstream for transmission, and channel coding is adopted to add parity bits to cope with drastic channel noise. This strategy demolishes the numeric properties within the video data and leads to the cliff effect. SoftCast avoids this by transmitting the real-value coefficients directly without bitstream transformation. In SoftCast, a novel error protection scheme was developed by scaling the magnitude of the transmitted coefficient. For a specific conventional 2D video sequence, consider applying 3D-DCT to every GOP. The resulting stream of DCT coefficients is divided into \(N\) chunks \(x_{1},x_{2},\ldots,x_{N}\) with size \(hxw\), hence \(x_{i}[j],j=1,\ldots,(hxw)\). The amount of information in each chunk is captured by its entropy (i.e., average energy) \(\lambda_{i}\). Each chunk \(x_{i}\) is scaled up to \(y_{i}[j]=g_{i}*x_{i}[j],g_{i}>1\) at the sender. The values \(y\) are then transmitted over the wireless channel. The channel noise is taken to be AWGN with zero mean and variance \(\sigma_{n}^{2}\). The received value becomes \(\hat{y}_{i}[j]=y_{i}[j]+n_{i}[j]\). To estimate the reconstructed signal \(\hat{x}_{i}[j]\) given \(\hat{y}_{i}[j]\), the linear least squares estimator (LLSE) is used:  
\[\hat{x}_{i}[j]=\frac{\lambda_{i}\hat{y}_{i}}{\lambda_{i}\hat{y}_{i}^{2}+\sigma_ {n}^{2}}\hat{y}_{i}[j] \tag{1}\]  
Consider how SNR changes the LMSE. At high SNR [11], the reconstructed signal \(\hat{x}_{i}[j]\) is estimated by simply scaling down the received signal, \(\hat{x}_{i}[j]=\hat{y}_{i}[j]/g_{i}\). For the scale up/down scheme, the reconstruction error is only \(\sigma_{n}^{2}/\hat{y}_{i}^{2}\) compared to \(\sigma_{n}^{2}\) for the direct transmission error. Therefore, this scheme remarkably enhances the transmission error protection when \(g_{i}\) is relatively large. Since the power budget for any transmission system is a constrained resource, scaling up some signal samples with more power means leaving other signal samples with less power. Therefore, power allocation is conducted to determine the optimal scaling factors for minimizing the total reconstruction distortion for the entire transmitted sequence. In [11; 18; 32], the optimal factor for scaling chunk \(i\) is:  
\[g_{i}=\lambda_{i}^{-1/4}\Big{(}\sqrt{\frac{P}{(\textit{lRxw})\sum_{i=1}^{N} \sqrt{\lambda_{i}}}}\Big{)} \tag{2}\]  
where \(P\) is the total power budget. The total reconstruction distortion under optimal power allocation is  
\[D=(\textit{lRxw})\sum_{i=1}^{N}\frac{\sigma_{n}^{2}}{\hat{y}_{i}^{2}}=\frac{( \textit{lRxw})^{2}\sigma_{n}^{2}}{P}\Big{(}\sum_{i=1}^{N}\sqrt{\lambda_{i}} \Big{)}^{2} \tag{3}\]  
From (2), it becomes clear that for traditional 2D video, the reconstruction distortion \(D\) is inversely related to the total power \(P\). The value of \(D\) can be computed once \(P\) is known. However, for 3D video, the power budget \(P\) is shared by texture videos and depth maps, which together determine the overall quality of the received 3D video. Hence, to optimally allocate the total power between texture videos and depth maps, the texture/depth power allocation ratio is estimated, considering the texture/depth distortion trade-off [29].