## 3 Our Contribution
### Systematic-RLNC Based Data Transmission System
#### 3.2.1 Systematic Random Linear Network Coding (SRLNC)
Receiving the sufficient packet combinations, the sink node performs decoding of the original transmitted packets and identifies the CM used to generate each packet combination. In case of multipath transmission, the final sink node collects a total of n packet combinations (\(\hat{x}_{1},\hat{x}_{2},\ \ldots\hat{x}_{n}\)), having linearly independent CVs, and thus the originally transmitted data packets from the source node are obtained as (66). \[\left[ \begin{matrix}\hat{S}_{1}\\ \hat{S}_{2}\\ \vdots\\ \hat{S}_{n}\end{matrix} \right]_{n\times 1}=\left[ \begin{matrix}\hat{q}_{1,1}&\hat{q}_{1,2 }&\ldots&\hat{q}_{1,n}\\ \hat{q}_{2,1}&\hat{q}_{2,2}&\ldots&\hat{q}_{2,n}\\ \vdots&\vdots&&\vdots\\ \hat{q}_{n,1}&\hat{q}_{n,2}&\ldots&\hat{q}_{n,n}\end{matrix} \right]_{n\times n }^{-1}\left[ \begin{matrix}\hat{x}_{1}\\ \hat{x}_{2}\\ \vdots\\ \hat{x}_{n}\end{matrix} \right]_{n\times 1} \tag{66}\]  
Applying the above-mentioned approach, our proposed systematic-RLNC scheme ensures packet error resilience, and thus outputs (66) are usually the same as the original packets transmitted. Undoubtedly, the proposed SRLNC algorithm works optimally so as to ensure higher throughput; however, realizing the need for a robust computationally efficient transmission system for UWSN, we made an effort to reduce CI. Reduction in the CI bits can enable a swift and computationally effective model for UWSNs. A brief of the CI bits' optimization is presented as follows:  
1. Optimization of the Coefficient Information Bits  
Considering the process of SRLNC based transmission over the proposed UWSN channel model, it can be observed that the selection of CV can make SRLNC more efficient to deliver bandwidth and time efficient transmission, which is vital for mission critical data transmission. We intend to select the best size of bits b needed to provide CV for efficient data transmission. In our model, the selection of b is performed in such a way that no packets are combined more than 2\({}^{\text{b}}\) times. To achieve this, we used a probe-packet generation based technique, where the individual packet contains m network coded packets. The number of bits assigned to b is increased continuously throughput generations and is continued in such a manner that the packet combinations belonging to the gth generation apply b = g bits so as to obtain the accurate elements of the uncompressed CIs. In case a source packet is combined more than 2\({}^{\text{b}}\) times at an intermediate node, the source node is informed for the generation of the specific packet combination that it belongs to. In this way, the source node applies the minimum number of bits b so that no intermediate node might combine a data packet more than 2\({}^{\text{b}}\) times. One of the key novelties of the proposed SRLNC scheme is that it applies the iterative buffer flush (IBF) mechanism that, after receiving ACK from the sink or receiver node, flushes its buffer to preserve bandwidth. It can enhance the resource utilization efficiency of the routing scheme. The following section discusses the SRLNC based UWSN routing protocol which has been simulated over the developed channel model.