## 3 Our Contribution
### Systematic RLNC Based UWSN
#### 3.3.2 SRLNC Based Routing Protocol  
The proposed routing protocol applies geographic route information on individual nodes to perform routing using SRLNC based transmission. To enable a simple transmission measure, the node nearest to the sink is considered as a data forwarding node that reduces the data loss probability significantly. Nodes apply the SRLNC transmission approach, where receiving N linear independently encoded packets, sink decodes the original transmitted data packets. As a simple solution, we applied a greedy forwarding model to estimate the best forwarding node.  
Consider \(\mathrm{n_{i}}\) to be the source node willing to transmit the data, \(\mathrm{N_{i}(t)}\) to be the \(\mathrm{n_{i}}\)'s neighboring nodes at certain time \(\mathrm{t}\), and \(\mathrm{S_{i}(t)}\) to be \(\mathrm{n_{i}}\)'s predefined or known sink nodes at time \(\mathrm{t}\). With node \(\mathrm{n_{i}\varepsilon N_{i}(t)}\), packet distribution is obtained as [4]:  
\[\mathrm{SPD}\big{(}\mathrm{n_{j}}\big{)}=\mathrm{D}(\mathrm{n_{i}},\mathrm{s_{ i}})-\mathrm{D}\big{(}\mathrm{n_{j}},\mathrm{s_{j}}\big{)} \tag{67}\]  
where \(\mathrm{D}(\mathrm{n_{i}},\mathrm{s_{i}})\) states \(\mathrm{n_{i}}\)'s Euclidean distance from its nearest sink \(\mathrm{s_{i}\in S_{i}(t)}\). The variable \(\mathrm{D}\big{(}\mathrm{n_{j}},\mathrm{s_{j}}\big{)}\) refers \(\mathrm{n_{i}}\)'s Euclidean distance to its nearest sink \(\mathrm{s_{i}\in S_{i}(t)}\). The higher packet  
Figure 1: Three-dimensional acoustic network structure.  
distribution states higher priority for the neighbouring node selection and, thus, at time t, the next hop forwarding node of \(n_{i}\) is  
\[C_{i}(t)=\left\{n_{j}\in N_{i}(t),\text{SPD}(n_{j}>0)\right\} \tag{68}\]  
For forwarding node \(n_{f}\in C_{i}\), \(D(n_{i},n_{f})\) presents the Euclidean distance between the source node \(n_{i}\) and the forwarding node \(n_{f}\). Let the probability of the data delivery of m bits over \(D(n_{i},n_{f})\) be \(p(D(n_{i},n_{f}),m)\). Then, the normalized packet distribution of \(n_{f}\) can be presented as:  
\[\text{NSPD}(n_{f})=\text{SPD}(n_{f})\times p(D(n_{i},n_{f}),m) \tag{69}\]  
Based on the respective node energy and the normalized packet spread (NSPD), a weighting model is derived that executes the forwarding nodes for further path selection:  
\[W=\partial\frac{E_{r}}{E_{o}}+(1-\partial)\text{NSPD} \tag{70}\]  
where \(\partial\) refers to the equivalence factor between the energy of a response node and NSPD. Among the other parameters in (70), \(E_{o}\) refers the initial energy, while \(E_{r}\) gives the residual energy of the response node. The weighing model (70) is applied to estimate the weight of the individual forwarding nodes where the candidate nodes with respective weight score are sorted in high to low order and updated to a matrix \(F_{i}(t)\). The first node having the highest weight score is selected as the data forwarding node to the sink. In case the first node fails in delivering the data, the next node in \(F_{i}(t)\) is selected as the forwarding node and it continues until the complete data are delivered to the sink. In such way, the q-th node in \(F_{i}(t)\) initiates transmitting if no preceding node has delivered data successfully within a defined duration \(T_{w}^{q}\) (71).  
\[T_{w}^{q}=T_{d}+\sum_{j=1}^{q}D\big{(}n_{j},n_{j+1}\big{)}/v+q\times T_{p} \tag{71}\]  
In (71), \(v\) represents the sound speed in water medium, \(T_{p}\) refers the processing time of the packets and parameter \(T_{d}=(R_{c}-D(n_{i},n_{f}))/v\) signifies the delay during data transmission.  
Applying best forwarding node (BFN) selection approach, the source node forwards the packet to the BFN, which is followed by SRLNC based data transmission over UWSN.  
Implementing the aforementioned approach, the packet delivery probability (PDP) is estimated as follows.