# Efficient On-Off Keying Underwater Acoustic Communication for Seafloor Observation Networks
## 3 Receiver Design Adapted to Channel
### IrCC Design under Rayleigh Fading Channel  
In many SON applications, the RSC was adopted as the channel coding scheme due to its low complexity [6; 8; 13]. When the channel condition is good, it achieves decent decoding performance [23; 24]. For a UAC channel with severe fading, however, it is no longer a good choice due to the high required-SNR threshold for reliable decoding. In other words, it cannot adjust to the channel. In Figure 3, the iterative decoding process is characterized via the well-known EXIT chart [25], where \(E_{\text{b}}/N_{0}=11.3\) dB and the RSC with the generating polynomial \((23,35)_{\text{s}}\) in octal indication is employed. The iterative tunnel between the EXIT curves of the ACC-OOK demapper and the soft decoder determines the performance and the convergence of the iterative decoding. Obviously, the iterative process is terminated in an early stage under the Rayleigh fading channel for the blocked iterative tunnel. To ensure an open tunnel, an increased \(E_{b}/N_{0}\) is needed and this may not be available in energy-constrained SONs. Therefore, we choose to use an IrCC to lower the SNR threshold for obtaining an open tunnel. The IrCC is designed as a weighted combination of 17 sub-codes with different rates \(R_{i}=0.1+0.05\left(i-1\right),i\in\left[1,17\right]\)[18], as shown in Figure 4. The information sequence of length \(k\) is divided into segments of length \(k_{i}\), which are respectively encoded by 17 sub-encoders, and then merged into the coding sequence. The 17 sub-codes are constructed by repeating and puncturing the mothercode defined by the generator \(\frac{1}{g_{0}}[g_{0},g_{1},g_{2},g_{3}]\), where  
\[ \begin{cases}g_{0}=1+D+D^{4}\\ g_{1}=1+D^{2}+D^{3}+D^{4}\\ g_{2}=1+D+D^{2}+D^{4}\\ g_{3}=1+D+D^{3}+D^{4}\end{cases}  \tag{9}\]  
To design an IrCC with target rate \(R\) is equivalent to designing the weighting coefficients \(\{\alpha_{i}\}\) for the sub-codes under the following constraint:  
\[ \begin{cases}\sum_{i=1}^{17}\alpha_{i}=1,&\alpha_{i}\in\left(0,1\right)\\ \sum_{i=1}^{17}R_{i}\alpha_{i}=R,&R_{i}\in\left[0.1,0.9\right]\\ \sum_{i=1}^{17}\alpha_{i}T_{1,i}\left(I_{\text{in}}\right)>T_{2}^{-1}\left(I_ {\text{in}},E_{\text{b}}/N_{0}\right),&I_{\text{in}}\in\left[0,1\right]\end{cases}  \tag{10}\]  
Figure 3: Premature terminated iteration of the system using RSC under the Rayleigh fading channel, \(E_{\text{b}}/N_{0}=11.3\) dB. where \(T_{1}\left(I_{\text{in}}\right)\) and \(T_{2}\left(I_{\text{in}},E_{\text{b}}/N_{0}\right)\) are the EXIT functions of the IrCC decoder and the ACC-OOK demapper, respectively. The distribution of \(\alpha_{i}\) determines the shape of the IrCC decoding curve, thus affecting the iterative decoding performance. For a fixed code rate, the goal is to keep an open iterative tunnel until the \(\left(1,1\right)\) endpoint. In other words, the IrCC decoding curve should match the ACC-OOK demapping curve, such that the \(E_{\text{b}}/N_{0}\) threshold for reliable decoding will be effectively reduced. The EXIT chart of the iterative process is shown in Figure 5, where the maximum mutual information optimized criterion [18] is adopted with a fixed code rate 0.5, and the optimized distribution of \(\left\{\alpha_{i}\right\}\) is: \(\left\{0.0012,0.0018,0.0028,0.0059,0.0178,0.1105,0.4690,0.0329,0.0338,0.0057,0.0254,\right.\)\(\left.0.0527,0.1035,0.0653,0.0294,0.0270,0.0153\right\}\). From the figure, the EXIT curve of the IrCC decoder matches that of the ACC-OOK demapper as expected, and thus the iterative tunnel is guaranteed, wherein the iterative trajectory deviates slightly from the iteration tunnel due to the limited interleaver depth [25]. Figure 4: Demonstration of IrCC encoding. Figure 5: Iteration trajectory of the system using IrCC under the Rayleigh fading channel, \(E_{\text{b}}/N_{0}=11.3\) dB. In Figure 6, the bit error ratio (BER) performances of the IrCC and the RSC(23,35) are compared under the Rayleigh fading channel. The number of iterations is 10.