## 3 UEP Using Spatial Modulation
### UEP Using Spatial Modulation  
The source coder used for underwater image transmission should be a low computational complexity encoder to manage the low power feeding of IoUTs nodes, and it must also attain a sufficient compression ratio performance to deal with underwater acoustic limited channel bandwidth. Therefore, many researchers provide a SPIHT coder as a best candidate for underwater image transmission [20; 21]. This subsection discusses the UEP technique using a SPIHT coder and SM scheme. The SPIHT coder outputs contain bitstream with unequal importance rank and significance as depicted in Figure 1[20]. Each encoded bit is more significant than the next one. In UEP using rate allocation, the bits with higher importance level are encoded with high redundancy channel coder [4; 6]. These significant bits are shown in Figure 2, to show the effect and contribution of each encoded bit of SPIHT encoder bitstream on PSNR of the reconstructed image. The bit error sensitivity (BES) of SPIHT encoder bitstream is achieved by primary encoding the original transmitted image using the SPIHT encoder and only one bit in the encoded image is corrupted, starting from the first bit to the last one. Each time a bit is corrupted, the encoded image is decoded and the resultant mean square error (MSE) is attained to evaluate its effect on the PSNR of reconstructed image. The corrupted bit is fixed before scheduled on to the next bit. Figure 2 shows the order of significance from the most significant types of bits to the least significant one of gray (\(256\times 256\)) Lena image encoded using SPIHT encoder to generate the source bitstream with a 0.5 bit rate comparison (0.5 bpp). The PSNR value of the reconstructed image is calculated using the following equation [6],  
Figure 1: SPIHT progressive source encoder. Figure 2: Error bit sensitivities within the SPIHT encoded bitstream. \[PSNR=10 log_{10}\left(\frac{\mathcal{M}_{\mathcal{G}}}{MSE}\right) \tag{24}\]  
\[MSE=\frac{1}{\mathcal{A}\times\mathcal{B}}\sum_{Tx(\cdot,\downarrow)}\sum_{Rx( \cdot,\downarrow)}\left[Tx(\cdot,\downarrow)-Rx(\cdot,\downarrow)\right]^{2} \tag{25}\]  
where \(Tx(\cdot,\downarrow)\) and \(Rx(\cdot,\downarrow)\) are the gray values of pixels in the transmitted and received images, respectively. \(\mathcal{A}\) and \(\mathcal{B}\) are image width and height, respectively, and \(\mathcal{M}_{\mathcal{G}}\) is the maximal gray value of the encoded image. As shown in Figure 2, the encoded SPIHT bitstream has unequal BES, therefore we can divide the output bitstream to two groups of bits based on its effect on the quality of reconstructed image. This group of bits can be critical and noncritical bits as shown in Figure 3. The \(N\) SPIHT encoded bits required to spread over the underwater channel will be divided into two groups, \(G_{1}\) and \(G_{2}\), and each group has different length of bits. As shown in Figure 4, the high significant critical group of bits \(G_{1}\) will be transmitted over the low ABER antennas indices carrying information unit and its length should not exceed the length of bits carried via the transmit antennas indices, and it can be written as  
\[G_{1}=\left\{b_{1},b_{2},b_{3},\ldots\ldots\ldots,b_{d}\right\}\text{, and }d=\left[\frac{\log_{2}(Nt)}{R_{SM}}\right]\star N \tag{26}\]  
The low significant encoded group of bits \(G_{2}\), which will be transmitted over SM signal constellations carrying information units can be given by  
\[G_{2}=\left\{b_{d+1},b_{d+2},\ldots\ldots\ldots,b_{N}\right\} \tag{27}\]  
As shown in UEP-SM scheme, Figure 4, the two groups of M-SPIHT bits, critical bits \(G_{1}\), and uncritical bits \(G_{2}\) are transmitted as follows; the critical group of bits \(G_{1}\) are carried via the antenna index information, and the uncritical group of bits \(G_{2}\) are carried via the constellation diagram information carrying units.