# Distributed Rateless Codes with Unequal Error Protection Property for Space Information Networks
## 2 System Model  
We consider a communication scenario in SIN as shown in Figure 1: two disjoint exploration rovers with sources \(s_{1}\) and \(s_{2}\) with data block of length \(k_{1}\) and \(k_{2}\) input symbols, respectively. Let \(S_{1}\) and \(S_{2}\) denote the set of \(s_{1}\) and \(s_{2}\) input symbols, respectively. \(S_{1}\) and \(S_{2}\) transmit to a base station \(D\) with the assistance of a periodic moving relay satellite/orbiter \(R\). Due to the periodic motion, \(R\) has limited access time, and the source nodes have the knowledge of the accessing period in the SIN. Note that, without loss of generality, the output symbols transmission in Figure 1 are on binary erasure channels (BEC), and the erasure probabilities between the four nodes are denoted by \(\varepsilon_{ij}\), where \(i\in\{1,2,R\}\) and \(j\in\{R,D\}\). Note that the qualities of direct links are much worse than the relay links in SIN, i.e., \(\{\varepsilon_{1D},\varepsilon_{2D}\}>>\{\varepsilon_{1R},\varepsilon_{2R}, \varepsilon_{RD}\}\). We define the relay links \(S_{1}-R\), \(S_{2}-R\), and \(R-D\) (Y-network in Figure 1) as primary links, and the direct links between sources to destination, \(S_{1}-D\), \(S_{2}-D\), as secondary links. We define each period of the relay in the SIN as a transmission session, and each transmission session period is divided into two _Phases_. In _Phase 1_, \(R\) is invisible to \(S_{1}\), \(S_{2}\), and \(D\), then \(S_{1}\) and \(S_{2}\) performs LT coding over their information set \(s_{1}\) and \(s_{2}\) with degree distribution \(\Omega_{1}(x)\) and \(\Omega_{2}(x)\), respectively, and transmits the coded symbols on the secondary links \(S_{1}-D\) and \(S_{2}-D\) to the destination \(D\); in _Phase 2_, once primary links \(S_{1}-R\) and \(S_{2}-R\) are available, the secondary link is closed to save energy immediately. \(S_{1}\) and \(S_{2}\) performs LT coding over its information set \(s_{1}\) and \(s_{2}\) with degree distribution \(\Psi_{1}(x)\) and \(\Psi_{2}(x)\), respectively, and transmits the coded symbols to the relay \(R\), and a rateless NC is performed at \(R\) and then transmitted to \(D\) on \(R-D\). The connections and durations are illustrated in Figure 2. The number of coded symbols transmitted on each link are denoted by \(N_{1}\) and \(N_{2}\). For this dynamic SIN network model, the detail of our DURC scheme is illustrated below:  
Figure 1: Dynamic multiple access SIN communications. Figure 2: Connections and durations of DURC in SIN relaying Communications. * _Initialization_ Suppose that the information symbol lengths of \(s_{1}\) and \(s_{2}\) are \(k_{1}\) and \(k_{2}\), respectively. The \(k_{m}\) (\(m\in\{1,2\}\)) symbols are divided into \(n\) subsets according to their importance levels, expressed as \(I_{m1},I_{m2},...,I_{mn}\) and \(k_{m}=\sum_{i=\,1}^{n}I_{mi}\), the fraction of the \(I_{mi}\) information symbols in \(k_{m}\) is \(\pi_{mi}\) and \(\sum_{i=\,1}^{n}\pi_{mi}\ =\ 1\). \(S_{m}\) selects the \(i\)-th importance level from subset \(I_{mi}\) with probability \(w_{mi}\), which is called symbol-selection weight [21]. \(S_{m}\) employs an LT-coding degree distribution \(\Omega_{m}(x)=\sum_{d_{m}=\,1}^{D_{m}}\Omega_{m,d_{m}}x^{d_{m}}\) in _Phase 1_, and \(\Psi_{m}(x)=\sum_{d_{m}=\,1}^{D_{m}}\Psi_{m,d_{m}}x^{d_{m}}\) in _Phase 2_, where \(D_{m}\) denotes a pre-selected maximum value of \(d_{m}\). * _Phase 1_\(R\) is invisible, and \(S_{1}\) and \(S_{2}\) generate distributed rateless coded symbols from \(k_{m}\) information symbols using LT-coding degree distribution \(\Omega_{m}(x)\), and transmit \(N_{1}\) coded symbols to \(D\) by secondary links. In an encoding process at \(S_{m}\), if a degree \(d_{m}\) is randomly selected with probability \(\Omega_{m,d_{m}}\) using the degree distribution \(\Omega_{m}(x)=\sum_{d_{m}=\,1}^{D_{m}}\Omega_{m,d_{m}}x^{d_{m}}\), then \(d_{m}\) information symbols are selected uniformly at random and are bitwise XORed to form the coded symbol.