# Energy-Efficient Channel Coding Strategy for Underwater Acoustic Networks
## 5 Results
### Signal-to-Noise Ratio Analysis  
In Figure 4, we analyze the energy consumption as a function of the operating SNR for a link distance of 1 km, assuming a target success delivery probability \(P_{s}^{*}=0.999\). This result considers optimized BCH codes for every SNR value.  
We can observe that the most efficiently operating SNR range in terms of energy consumption is between 10 dB and 15 dB for all link distances. For SNR values smaller than 10 dB, the energy consumption increases. This occurs because the FER increases and consequently the number of code packet transmissions required by the fountain code to correctly deliver the \(M\) information-bearing packets. On the other hand, for SNR values above 15 dB, it is necessary to excessively increase the transmit power, which also leads to an increasing energy consumption. In practice, however, an  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline \(k\) & Spreading Factor & 1.5 \\ \(s\) & Shipping Activity & 0.5 \\ \(w\) & Wind Speed (m/s) & 0 \\ \hline \(B\) & Channel Bandwidth (Hz) [30] & 320 \\ \(R_{b}\) & Bit Rate (bits/s) [30] & 160 \\ \(P_{t}\) & Transmit Power (dB re \(\cdot\)Pa) & 120–190 \\ \hline \(\varphi\) & Efficiency of the Power Amplifier (PA) + Transducer [31] & 0.25 \\ \(p\) & Frame Payload (bytes) [30] & 128 \\ \hline \(M\) & Number of Data Packets per Fountain Coding Round [16] & 10 \\ \(P_{s}\) & Target Success Delivery Probability [16] & {0.999, 0.8} \\ \hline \(\
u\) & \(K\)-distribution Shape Parameter [29] & 1.5 \\ \(\alpha\) & \(K\)-distribution Scale Parameter [29] & \(\
u^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: System parameters.  
acoustic modem imposes limits to the maximum transmit power. Therefore, depending on the link distance, we cannot always achieve the optimal required SNR at the receiver.  
Figure 5 shows the optimal FEC code rate \(r=k/n\) and the error correction capability \(t\), as a function of the SNR for a frame size \(p=128\) bytes and link distance of 1 km. The target success delivery probability is \(P_{s}^{*}=0.999\). When the receiver operates with a higher SNR, the optimal rate approaches one, which indicates the need for lower redundancy because the link probability of error is very small. A similar behavior in terms of optimal code rate selection was observed for other link distances, whose results were omitted for sake of brevity.  
Figure 6 shows the exact selection of parameters \(k\) and \(n\) associated with the optimal coding rate \(r\) shown in Figure 5. It is important to point out that, in the intervals 10-15 dB and 45-50 dB, the selected  
Figure 4: Energy consumption versus operating SNR.  
Figure 5: Optimal BCH code rate versus SNR for \(P_{s}^{*}=0.999\).  
code rate was \(r_{1}=k/n=247/255\) instead of \(r_{2}=502/511\). The reason is that \(r_{1}\) is a little smaller than \(r_{2}\), which causes a small reduction in terms of energy consumption.  
Figure 7 shows the energy consumption for all FEC codes in Table 1, assuming a specific SNR of \(E_{b}/N_{0}=44\) dB. The \(x\)-axis represents code index, starting from code \((n,k,t)=(7,4,1)\) (code index 1) up to \((n,k,t)=(511,10,121)\) (code index 127). The main idea is to show the energy consumption level generated by each code if it is used in the transmission system. The operation SNR value of \(E_{b}/N_{0}=44\) dB was chosen by didactic methods. At this SNR level, all BCH codes are feasible choices, leading to reasonable values of energy consumption. The same analysis could be done for lower SNR values; however, in this case, not all of the codes of Table 1 could be used because the energy consumption is very high for some of them due to the number of required transmissions at the L3 layer. The red dashed line indicates the optimal code selection for operation at \(E_{b}/N_{0}=44\) dB.  
Figure 6: Optimal BCH parameters.  
Figure 7: Energy consumption for different codes at a fixed SNR.