# Distributed Rateless Codes with Unequal Error Protection Property for Space Information Networks
## 4 Simulation and Comparison  
Let us investigate the DURC parameters under a totally symmetric network model, where the block lengths are \(N_{1}=N_{2}=1200\), the information symbols lengths are \(k_{1}=k_{2}=1000\), and the erasure probabilities of channel links are \(\varepsilon_{1D}=\varepsilon_{2D}=0.5\), \(\varepsilon_{1R}=\varepsilon_{2R}=0\), and \(\varepsilon_{RD}=0.1\). Setting the maximal value of the degree \(D_{1}=D_{2}=50\), desired total overhead \(\gamma*=1.1\), the proportion of MIB in every source is \(\pi_{m1}=0.5\), and the decoding performance relationship between MIB and LIB is \(I_{m,1}\geq 10I_{m,2}\). To obtain the optimized degree distribution \(\Psi_{1}(x)\) and \(\Psi_{2}(x)\), we solved the MOP1 and finally get a Pareto front about the optimized \(y_{l,12}\) and \(y_{l,22}\). We plot the Pareto fronts obtained from our optimizations in Figure 4, where \(\eta=y_{l,2,2}/y_{l,1,2}\). It is obviously that the protection of \(S_{1}\) is increasing with the increasing of \(\eta\). The partial optimization results are shown in Table 1. Furthermore, we select an equal error protect (eep) degree distribution from the sets of our optimized DURC scheme, i.e., \(\eta=1\) and \(n=1\), the optimized \(\Psi_{1}(x)\) and \(\Psi_{2}(x)\) at sources are identical as \(\Psi_{1}(x)=\Psi_{2}(x)=0.0111x+0.4944x^{2}+0.1787x^{3}+0.1653x^{5}+0.0053x^{6}+ 0.0978x^{12}+0.0474x^{50}\). Furthermore, we substitute \(\Psi_{m}(x)\) into the MOP problem (12) with a desired total overhead \(\gamma^{*}=1.1\) to solve for the RC degree distribution on secondary links as \(\Omega_{1}(x)=\Omega_{2}(x)=0.054x+0.946x^{2}\), and NC relaying probabilities as \(p_{1}=0.045\), \(p_{2}=0.045\) and \(p_{3}=0.91\), and we can use these eep-DURC scheme to compare with three existing distributed rateless coding schemes in the same network model as described before. The store-and-forward (SF) scheme is that the RC degree distributions on secondary and primary links are both set as the classical degree distributions used for Raptor codes in [9], and the relay node \(R\) randomly forwards the received coded symbols from \(S_{1}\) and \(S_{2}\) with equal probability. Simple network coding scheme (XOR) is that \(R\) always sends a new coded symbol to \(D\), which is generated by XORing the two coded symbols from \(S_{1}\) and \(S_{2}\). The SLRC scheme uses the network coding relay protocol as in [18], the relay node \(R\) only forwards coded symbols with degree-1 and degree-2 with a threshold probability, and RC degree distributions on secondary and primary links are also the Raptor degree distributions. Figure 4: Connections and durations of DURC in SIN relaying communications. Figure 5a shows the DER versus the total overhead for various distributed rateless codes (DRC) schemes, which are obtained by the asymptotical performances formed by And-Or tree analysis. It is noted that the XOR scheme has the worst decoding performance because of the lack of lower degree symbols (1 and 2) received by \(D\). The SLRC scheme has better performance than the SF scheme when the overhead is larger than 1.15. The DER of the eep-DURC scheme, which is the basic of our proposed UEP, is clearly the lowest. Figure 5b shows the DER versus the total overhead for various UEP schemes. It is noted that the DURC schemes achieved the lowest DER for both MIB and LIB, which gives great support for information transmission in SIN. Figure 6a shows the DER versus the total overhead of inner information in one source node for DURC and eep-DURC schemes from the And-Or tree performance evaluation. It is obvious that the DURC scheme can achieve marvel decoding performance of MIB with about two orders of the decoding performance of LIB decreasing, which gives great protection for MIB than eep-DURC scheme. Figure 6b shows the LIB performance of different sources for \(\eta=10,10^{2},10^{3},10^{4}\).