## 6 Simulation and Comparison
### Performance of the RC IR-HARQ Transmission Scheme  
In this subsection, we simulate the performance of our RC IR-HARQ transmission scheme, the Monte Carlo simulation result of the average number of transmissions of data blocks with the PCPP coding scheme is present. The system parameters are the same as provided in Table 3, and the rest of the simulation parameters  
Figure 5 shows the average number of transmissions of our RC IR-HARQ scheme and the RCP scheme for a sequential of 100 data blocks transmission in 3 cases with the initial channel capacity \(I^{(1)}(W)=0.5\). Our RC IR-HARQ scheme can reduce half of the average number of transmissions than the RCP scheme as shown in Figure 5a, and also significant less than the RCP scheme in Figure 5b,c. Because all the initial code-rates of the data blocks in the RCP scheme are equal to \(R_{1}^{(1)}=0.8\), the average number of transmissions for the sequential data blocks is substantially equal to the first data block, and the successful transmission of previous data block does not help enhance the efficiency of the next ones. Therefore, the average number of transmissions in the RCP scheme is about 2.8 times in Case 1 as shown in Figure 5a, and 3.5 times in Case 2 as shown in Figure 5b, and 2.7 times in Case 3 as shown in Figure 5c. In contrast with the RCP scheme, our RC IR-HARQ scheme is more adaptable to the continuously data blocks transmission. The PCPP codes for the 1 st data block are with the initial code-rate \(R_{1}^{(1)}=0.8\) PCPP coding block; then, the optimal initial code-rate of the PCPP codes for the continuously data block transmission can be determined in different cases as discussed in Section 5.2. Therefore, after the 1 st data block transmission, the average number of transmissions of our RC IR-HARQ scheme is rapidly decreased compared to the RCP scheme. The average number of transmissions in the RC IR-HARQ scheme is about 1.8 times in Case 1, as shown in Figure 5a, and 2.4 times in Case 2, as shown in Figure 5b, and 2.5 times in Case 3, as shown in Figure 5c, which is verified by our theoretical analysis, as shown in Table 2. It is worth noting that our RC IR-HARQ scheme has  
Figure 5: The comparison of the average number of transmissions of 100 data blocks in our RC IR-HARQ scheme and the RCP scheme with initial channel capacity \(I^{(1)}(W)=0.5\) in three cases: (a) Case 1: \(\Delta R_{1}=0.2\); (b) Case 2: \(\Delta R_{2}=0.1\); (c) Case 3: \(\Delta R_{3}=0.25\). Case 1, which means the accurate statistical information of the time-varying channel can help the PCPP encoding and decoding in the RC IR-HARQ transmission scheme, and it can help joint optimization with the channel estimation. Moreover, we simulate the performance with different initial channel capacity \(\boldsymbol{I^{(1)}(W)}\) in Case 1 as shown in Figure 6, where \(\boldsymbol{I^{(1)}(W)}\) is 0.3, 0.4, 0.6, and 0.7, and other simulation parameters are the same as is given in Table 4. The average number of transmissions in the RCP scheme are 3.8 times, 3.1 times, 2.2 times, and 1.8 times in Figure 6a-d, respectively. Obviously, the average number of transmissions of the RCP scheme is strongly dependent on the difference between \(\boldsymbol{R_{1}^{(1)}}\) and the \(\boldsymbol{I^{(1)}(W)}\), as shown in Figure 6a-d. It is worth noting that the average number of transmissions in both schemes is about 1.8 times when \(\boldsymbol{I^{(1)}(W)=0.7}\), as shown in Figure 6d. Because the initial code-rates in Case 1 is \(\boldsymbol{R_{1}^{(1)}=0.8}\), and \(\boldsymbol{\Delta R_{1}=0.2}\) for both schemes, when \(\boldsymbol{I^{(1)}(W)=0.7}\), both schemes can finish the transmission in no more than two time transmissions. In our RC IR-HARQ scheme, the average number of transmission in Figure 6 are all about 1.8 times under different \(\boldsymbol{I^{(1)}(W)}\), which proves that our scheme can perform well over the time-varying channel if the sender has statistical information on the channel.