## 5 Simulation Model and Results
### Optimum Number of FEC Packets, Nmx  
The effect of splitting the FEC part, into multiple FEC packets, on throughput efficiency and energy efficiency is shown in Figure 5a,b, respectively. For this analysis, the above achieved optimum payload size is used in a region with 5 _CNodes_ distributed randomly at each run.  
From Figure 5a, it is clear that throughput efficiency decreases as \(N_{mx}\) is increased above 2. This is mainly because with more FEC fragments the total amount of time taken to transfer the required amount of FEC information to the destination increases; due to the accumulation of long propagation delays associated with each _NACK_ and FEC packet transmission. The best throughputs are achieved at  
Figure 5: **(a)** Throughput efficiency _vs._ number of FEC packets (\(N_{mx}\)); **(b)** Energy efficiency _vs._\(N_{mx}\).  
the values of \(N_{mx}=1\) and 2, with \(N_{mx}=1\) providing slightly better value. Thus it is clear that in the presence of long propagation delays it is better to transmit the FEC information in only one or two FEC packets than dividing it into many.  
On the other hand, in terms of energy efficiency, the transmission of many smaller FEC packets does not rapidly degrade the performance (from Figure 5b). Transmission of smaller FEC packets, one-by-one, allow only up to the required amount of FEC information being sent to the destination, thus preventing the energy consumption from transmission of extra FEC bits. However, more number of FEC packets increases the total number of Viterbi decoding attempts, which take place every time a new packet is received, thus adding to the overall energy consumption. Because of these two opposing factors the energy efficiency does not show much deviation with an increase in \(N_{mx}\). However at \(N_{mx}=3\) and \(N_{mx}=4\), slight irregularities are, most probably, because of the puncturing patterns used during the simulations, but they are irrelevant to this analysis. The puncturing patterns used for generating FEC packets are shown in Table 2. The convolution code with the patterns used at \(N_{mx}=4\) seems to perform equally better as that at \(N_{mx}=3\), especially in terms of energy efficiency.  
The 95% confidence interval shown at any point in Figure 5, let's say \(N_{mx}=1\), is obtained over a total of 100 runs each delivering 1,000 packets. The average value of the throughput efficiency, obtained over 100 \(\times\) 1,000 values, is found to be 0.0415 with a standard deviation of 0.0268. Then using the general principle of 95% confidence interval calculation, the one-sided interval can be approximated to 0.0002, thus resulting in the lower and upper 95% confidence levels of 0.0413 and 0.0417, respectively. Though not shown in other plots, the same confidence level applies for all other figures with number of runs varying from 100 to 150, and number of data packets varying from 1,000 to 1,500. Finally, utilising the results in Figure 5a and 5b simultaneously, we choose \(N_{mx}=2\) to be the  
\begin{table}
\begin{tabular}{c c c} \hline \hline _No. of FEC_ & \multirow{2}{*}{_FEC Packet_} & _Puncturing Pattern Used for Generating_ \\ _Packets_ & & _the Related FEC Packet_ \\ \hline \(N_{mx}=0\) & _Pac_-0 & 10101010101010101010 \\ \hline \(N_{mx}=1\) & _Pac_-1 & 01010101010101010101 \\ \hline \(N_{mx}=2\) & _Pac_-1 & 01000100010001000100 \\ \(N_{mx}=2\) & _Pac_-2 & 00010001000100010001 \\ \hline \(N_{mx}=3\) & _Pac_-1 & 01000001000001000001 \\ \(N_{mx}=4\) & _Pac_-3 & 0000100000010000001000 \\ \(N_{mx}=5\) & _Pac_-4 & 00000010000000100000 \\ \hline \(N_{mx}=5\) & _Pac_-3 & 000001000000000100000 \\ \(N_{mx}=6\) & _Pac_-4 & 000000010000000010000 \\ \hline \(N_{mx}=7\) & _Pac_-4 & 0000000100000000010000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Puncturing Patterns.  
optimum value for number of FEC packets, whose energy efficiency is better than that of \(N_{mx}=1\), with negligible difference in their throughput efficiencies.