## 3 Performance Evaluation
### OP at Each User  
In the Cov-Scm scheme, we first denote \(r_{2}\) as the number of packet \(p_{1}\) that \(\text{SS}_{2}\) successfully receives after the transmission from \(\text{SS}_{1}\) is complete. As mentioned above, if \(r_{2}<H_{\text{min}}\), \(\text{SS}_{2}\) cannot recover the data \(m_{1}\), resulting in an outage at \(\text{SS}_{2}\). Therefore, we can formulate OP at \(\text{SS}_{2}\) as  
\[\text{OP}_{2}^{\text{Cov-Scm}}=\sum_{r_{2}=0}^{H_{\text{min}}-1}C_{N_{\text{ max}}}^{r_{2}}(1-\Phi_{1})^{r_{2}}(\Phi_{1})^{N_{\text{max}}-r_{2}}, \tag{19}\]  
where \(C_{N_{\text{max}}}^{r_{2}}\left(C_{N_{\text{max}}}^{r_{2}}=\frac{N_{\text{ max}}!}{r_{2}!(N_{\text{max}}-r_{2})! }\right)\) is the binomial coefficient in NewTon expansion, and also represents the total number of possible cases in which \(\text{SS}_{2}\) can decode correctly the \(p_{1}\) packet. Then, substituting Equation (18) into Equation (19), we obtain expression of OP at \(\text{SS}_{2}\). Similarly, OP at \(\text{SS}_{1}\) can be given as  
\[\text{OP}_{1}^{\text{Cov-Scm}}=\sum_{r_{1}=0}^{H_{\text{min}}-1}C_{N_{\text{ max}}}^{r_{1}}(1-\Phi_{2})^{r_{1}}(\Phi_{2})^{N_{\text{max}}-r_{1}}. \tag{20}\]  
In the Mod-Scm scheme; assume that the source \(\text{SS}_{i}\) transmits its data first. Similarly to Equations (19) and (20), OP of \(\text{SS}_{j}\) can be calculated as  
\[\text{OP}_{j}^{\text{Mod-Scm}}=\sum_{r_{j}=0}^{H_{\text{min}}-1}C_{N_{\text{ max}}}^{r_{j}}(1-\Phi_{i})^{r_{j}}(\Phi_{i})^{N_{\text{max}}-r_{j}}. \tag{21}\]  
As mentioned above, let \(N_{i}\) denote the number of transmission of \(\text{SS}_{i}\), where \(H_{\text{min}}\leq N_{i}\leq N_{\text{max}}\). If \(N_{i}<N_{\text{max}}\), this indicates the \(\text{SS}_{j}\) source can gather enough \(H_{\text{min}}\) packets \(p_{i}\) before \(\text{SS}_{i}\) reaches its maximum transmission times \((N_{\text{max}})\). The probability that \(\text{SS}_{j}\) obtains enough \(H_{\text{min}}\) packets \(p_{i}\) after \(N_{i}\) attempts of \(\text{SS}_{i}\) is computed as  
\[\Pr\bigl{(}r_{j}=H_{\text{min}}\big{|}N_{i}<N_{\text{max}}\bigr{)}=C_{N_{i}-1} ^{H_{\text{min}}-1}(1-\Phi_{i})^{H_{\text{min}}}(\Phi_{i})^{N_{i}-H_{\text{min}}}. \tag{22}\]Equation (22) can be explained that after the \((N_{i}-1)-\text{th}\) transmission of \(\text{SS}_{i}\), \(\text{SS}_{j}\) must receive successfully \((H_{\text{min}}-1)\) packets \(p_{i}\), and the probability of this event is given as \(C_{N_{i}-1}^{H_{\text{min}}-1}(1-\Phi_{i})^{H_{\text{min}}-1}(\Phi_{i})^{N_{i}- H_{\text{min}}}\). Then, at the \(N_{i}-\text{th}\) transmission of \(\text{SS}_{i}\), \(\text{SS}_{j}\) decodes correctly \(p_{i}\), and hence, we obtain Equation (22). Next, we consider the case where \(N_{i}=N_{\text{max}}\), and this case occurs when \(\text{SS}_{j}\) correctly receives at most \((H_{\text{min}}-1)\) packets \(p_{i}\) after \((N_{\text{max}}-1)\) transmission times of \(\text{SS}_{i}\). As a result, we can calculate the probability of this case as  
\[\Pr(N_{i}=N_{\text{max}})=\sum_{r_{j}=0}^{H_{\text{min}}-1}C_{N_{\text{max}}-1 }^{r_{j}}(1-\Phi_{i})^{r_{j}}(\Phi_{i})^{N_{\text{max}}-1-r_{j}}. \tag{23}\]  
We now consider OP at \(\text{SS}_{i}\) under condition that the maximum number of transmissions of \(\text{SS}_{j}\) is \(2N_{\text{max}}-N_{i}\); similar to (19)-(21), we have  
\[\text{OP}_{i|N_{i}}^{\text{Mod-Scm}}=\sum_{r_{i}=0}^{H_{\text{min}}-1}C_{2N_{ \text{max}}-N_{i}}^{r_{j}}\big{(}1-\Phi_{j}\big{)}^{r_{i}}\big{(}\Phi_{j} \big{)}^{2N_{\text{max}}-N_{i}-r_{i}}. \tag{24}\]  
From Equations (22)-(24), OP at \(\text{SS}_{i}\) can be expressed as follows:  
\[