## 8 Conclusions  
In this paper, we presented a novel multiple-access network with a cooperative relay and proposed a novel enhanced distributed fountain coding scheme based on it. Moreover, we derived the overall degree distributions and analyzed the decoding performance of the proposed EDFC asymptotically by employing the And-Or tree method. Furthermore, we proposed a design method of degree distributions using joint iterative optimization algorithms. Simulation results show that the proposed EDFC obtains better BER performance than the existing GDFC on lossless channels. Moreover, EDFC is able to obtain a good performance at a moderate erasure probability, such as \(\text{BER}=4.3\times 10^{-5}\) when \(p_{rd}=0.3\) and \(p_{sr}=0.3\). It reveals that the introduction of an extra cooperative relay will not only improve the performance of the sources connected to this cooperative relay but will also enhance the overall performance for all sources and provide a UEP property for different sources. With the additional cooperative relay, EDFC is able to overcome the effects of bad channel conditions caused by terrain, obstacles, and so on to avoid communication interruptions and improve the reliability of the network. In the future, we will study the application of EDFC in wireless sensor networks and consider dynamic network models where cooperative relays are movable and investigate feasible fountain coding schemes.  
Conceptualization, H.S. and H.Z.; methodology, H.S. and J.B.; software, H.S. and J.B.; investigation, H.S. and H.Z.; writing--original draft preparation, H.S.; writing--review and editing, H.S.; funding acquisition, H.S. and H.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded in part by the National Natural Science Foundation of China (Grants No. 92067201, 61871446), in part by the Jiangsu Provincial Key Research and Development Program (Grants No. BE2020084-1, BE2020084-3), and in part by the NUPTSF (Grants No. NY215031, NY217032).  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & \multicolumn{2}{c}{**Advantages**} & \multicolumn{2}{c}{**Disadvantages**} \\ \hline \multirow{3}{*}{Decode-and-forward (DF)} & \(\bullet\) & Easy to implement & \(\bullet\) & Large latency \\  & \(\bullet\) & No requirement for optimization & \(\bullet\) & High complexity \\  & \(\bullet\) & Easy to implement & \(\bullet\) & Error propagation \\ \multirow{3}{*}{DLT} & \(\bullet\) & Easy to implement & \(\bullet\) & Unoptimized degree distributions \\  & \(\bullet\) & Low complexity & \(\bullet\) & Unable to provide UEP property \\ \multirow{3}{*}{GDFC} & \(\bullet\) & Low BER & \(\bullet\) & Communication interruptions due to bad channel conditions \\  & \(\bullet\) & UEP property & & Channel conditions \\  & \(\bullet\) & Flexible parameter settings & \(\bullet\) & Increased complexity due to optimization \\ \multirow{3}{*}{EDFC} & \(\bullet\) & Lower BER & \(\bullet\) & Additional hardware cost \\  & \(\bullet\) & High reliability & \(\bullet\) & Increased complexity due to optimization \\ \multirow{3}{*}{EDFC} & \(\bullet\) & Enhanced UEP property & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of decode-and-forward, DLT, GDFC, and EDFC.