## 3 Protocols' Simulation  
The CSR-ARQ protocols were simulated and compared with the traditional GBN-ARQ and SR-ARQ solutions [24; 27]. In the existing works, the GBN-ARQ and SR-ARQ schemes were implemented using bidirectional links; that is, the uplink and downlink used the same medium. In this paper, as a comparison, the GBN-ARQ and SR-ARQ schemes used different links for uplink ARQ packets and downlink data; that is, the uplink used the underwater acoustic channel transmission and the downlink used the visible light channel transmission. The ultimate goal of the error-free data transmission protocol for optical-acoustic cooperative communication is to ensure the error-free transmission of UWVLC and improve the effective data throughput of visible light communication as much as possible under the condition of low-speed underwater acoustic ARQ feedback. The throughput of the ARQ systems is defined as the ratio of the total amount of data transmitted \(S\) (bits) to the time it takes to complete the transmission \(T\) (sec).  
\[Throughput=\frac{S(bits)}{T(sec)} \tag{3}\]  
In the simulation, we fixed the file size to 750 kB, set the packet loss rate from 0.001 to 0.5, and counted the time taken for the file to be transmitted without errors under different packet loss rates. Then we calculated the system throughput. It should be noted that the packet loss rate here refers to the ratio of the number of lost frames in the optical communication transmission data frame to the total number of transmission frames. For  
Figure 9: Data mapping relationship of CSR-ARQ.  
CSR-ARQ, data frames were reassembled into packets, but the Packet Loss Rate set in the simulation was still the data frame loss rate. The average of 100 independent simulations is shown in Figure 10a.  
The simulation results showed that the throughput of the CSR-ARQ scheme was significantly better than the GBN-ARQ scheme and SR-ARQ scheme, when the packet loss rate was in the range of 0.01-0.1. Furthermore, with the increase in the packet loss rate, the throughput of the CSR-ARQ scheme also dropped more gently. The throughput of the SR-ARQ scheme decreased significantly with the increase in the packet loss rate. This is because the flag array of the underwater acoustic feedback can only mark the positions of 13 unsuccessfully received data frames. That is, each feedback can only retransmit up to 13 data frames, which greatly limits the transmission efficiency.  
In order to further investigate the impact of the transmission file size on different schemes, we set the packet loss rate to 0.1. Figure 10b shows the results of the throughput of each scheme as a function of the file size.  
It can be seen that in the case of different file sizes, the throughput of the CSR-ARQ scheme was better than that of the GBN-ARQ scheme and the SR-ARQ scheme, and its peak value was in the range of file sizes of 750-1000 kB. However, when the file size exceeded 1000 kB, the throughput of the CSR-ARQ solution decreased significantly as the file increased, while the throughput curve of the other two solutions was relatively stable. The reason is that these two schemes do not re-combine optical communication data frames compared with CSR-ARQ. This approach enables it to accurately locate the location of the lost packets and does not change with the file size, but this is at the expense of the number of lost packets. The location of packet loss in the CSR-ARQ solution was relatively ambiguous, and the location accuracy varied with the file size. Limited by the length of the underwater acoustic communication data frame, the SR-ARQ scheme could only obtain the positions of 13 missing packets in one feedback, and the efficiency was severely restricted.