## 4 The Proposed Selective Retransmission Mechanism
### Energy Consumption  
The energy consumption for processing/transmission of every single bit depends on the hardware characteristics of the employed sensors. However, such characteristics do not affect the experiments, since they will be considered for all tests. The parameters for energy consumption computation are based on [15, 21], as presented in Table 2.  
The DWT processing in each source node for the image in Figure 5 consumes 150.6 mJ for a 1-level 2D DWT and 188.3 mJ for a 2-level 2D DWT, when the parameters in Table 2 are considered. Such energy is always accounted when assessing the energy consumption of the proposed approach. Initially, we analyzed the energy consumption as a function of the number of hops that compose the path from the source to the sink. For simplicity, we considered that all nodes have the same transmission range (50 meters), and the previous (\(h\) - 1) and next (\(h\) + 1) hops are both in the transmission range of hop \(h\). \begin{table}
\begin{tabular}{|c|c|} \hline
**Variable** & **Value** \\ \hline \(e_{e}\) & \(50\times 10^{-9}\) J/bit \\ \hline \(e_{t}\) & \(100\times 10^{-12}\) J/bit/m\({}^{2}\) \\ \hline \(e_{shift}\) & 3.3 nJ \\ \hline \(e_{add}\) & 3.3 nJ \\ \hline \(e_{read}\) & 0.26 uJ \\ \hline \(e_{write}\) & 4.3 uJ \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters for the experiments. Figure 5: Original image for the experiments. Figure 6(a) shows the overall energy consumption (mJ) when the mean PER is 5% (\(b=0.9994\) and \(g=0.99998\)) for all links between neighbor intermediate nodes, while Figure 6(b) considers the mean PER of 15% (\(b=0.99987\) and \(g=0.99998\)). Three different transmission approaches were considered: fully-reliable, selective retransmission for 1-level 2D DWT and selective retransmission for 2-level 2D DWT, respectively based on equations in Equations (6), (20) and (27). For the subbands HL\({}_{(2)}\), LH\({}_{(2)}\) and HH\({}_{(2)}\) produced by a 2-level 2D DWT in both tests, DR = (\(H_{p}\)/2). It is also assumed that all packets are transmitted with DR=0 for the traditional fully-reliable transmission approach. The initial obvious conclusion is that the energy consumption increases when packets have to cross more intermediate nodes. Moreover, it is interesting to note that higher PER results in energy saving for the proposed approach when compared with the lower PER case, as most data (75%) are unreliably transmitted (DR = 255) over the path, in a different way of the fully-reliable approach. As we did not consider the energy costs of any coding technique for the fully-reliable transmission mechanism, the proposed solution is less energy-efficient for communications over very short paths, since DWT energy costs have to be accounted. However, such behavior changes when packets have to cross more hops, and it is more evident for higher mean PER. Additionally, even following the fully-reliable paradigm some image coding may be required, also demanding energy of source nodes. There is also an interesting difference between transmissions for packets generated after 1-level and 2-level 2D DWT. The transmission of packets using the semi-reliable transmission service is only advantageous for larger paths and for higher PER, since 2-level 2D DWT consumes more energy than 1-level 2D DWT. When the fully-reliable transmission mechanism is employed, we expect that, on average, every intermediate node consumes an equivalent amount of energy. However, the energy consumption in each intermediate node is likely to be different for the proposed selective retransmission mechanism, since packets that are lost and not retransmitted in previous hops do not consume energy in subsequent hops in the path to the sink. Considering the same mean PER of the last experiments, Figure 7 presents  
Figure 6: Energy consumption over the path. the energy consumption (mJ) in each hop for a path with 10 intermediate nodes, testing three different values of DR for semi-reliable transmission.