# Energy-Efficient Channel Coding Strategy for Underwater Acoustic Networks
## 5 Results
### Link Distance Analysis  
In Figure 8, we show the optimal code rate as a function of the link distance, assuming a transmit power \(P_{t}=160\) dB re \(\mu\)Pa. The results consider two values for the target success delivery probability, \(P_{s}^{*}=0.999\) and \(P_{s}^{*}=0.8\). The required coding rate reduces with the distance, which means that we require a more powerful code for larger distances as the transmit power is limited. If the system is allowed to operate with a lower target success delivery probability (\(P_{s}^{*}=0.8\)), the link can use a higher coding rate, saving energy. Figure 9 shows the optimal parameters \(k\) and \(n\) for both values of \(P_{s}^{*}\). Observe that in the distance range between 12 and 14 km, the selected codeword size was \(n=255\) instead of \(n=511\), as previously discussed. Figure 10 shows the optimal FEC parameters for a reduced block size of \(p=128\) bits. In essence, the general conclusions are the same as for the case of \(p=1024\) bits, with the main difference that, when considering \(p=128\), the optimal choices of \(k\) and \(n\) are much more diverse than from those in the case of \(p=1024\).  
Figure 8: Optimal coding rate versus distance.  
Figure 9: Energy consumption versus operating SNR (\(p=1024\) bits).  
In Figure 11, we present a comparison of three different schemes in terms of energy consumption. The first one uses an uncoded L2 layer, while the second one uses a fixed code rate at the L2 layer (\(r=1/2\)); finally, the third one is the proposed mixed scheme with an optimized FEC coding rate. Note that the three schemes use the same fountain code.  
For the uncoded scheme at the L2 layer, the energy consumption increases 30 times when the link distance goes from 1 km to 2 km, for both values of \(P_{s}^{*}\). In the second scheme, when a fixed code rate (\(r=1/2\)) is employed, we can observe two distinct performance phases. From 1 km to 8 km, the energy consumption is kept constant because the channel code is able to compensate for the SNR  
Figure 11: Energy consumption versus distance.  
Figure 10: Energy consumption versus operating SNR (\(p=128\) bits).  
degradation which occurs when the distance increases. The energy consumption at this point is above the consumption that would be achieved with an optimized scheme because the choice of the fixed rate \(r=1/2\) is not optimal. For link distances beyond 8 km, the channel degradation is too severe, which results in an increased number of coded packets transmitted at the L3 layer. This results in a fast increase in the energy consumption. The third scheme uses the proposed mixed coding strategy with optimized code rate. In such a case, we achieve the best performance among the three options for the two target success delivery probabilities under analysis.  
Based on the numerical results, we can determine the parameters \((n,k,t)\) that must be chosen for a particular communication link. These parameters can be determined either from the average signal-to-noise ratio (SNR) or the link distance. From the practical point of view, the choice of BCH parameters can be performed in the planning phase or in the operating phase of the network. In the UAN planning phase, the parameters can be chosen based on the link distance between two nodes. During the network operation phase, the BCH code parameters can be negotiated between two nodes by using, for instance, a control protocol. The idea is to initially estimate the average received SNR and then select the respective optimized BCH code parameters. Considering the case where \(p=1024\) bits (128 bytes), the parameters \(n\) and \(k\) are obtained from Figures 6 and 9. The error correction capability, \(t\), can be read from Table 1.