# Distributed Rateless Codes with Unequal Error Protection Property for Space Information Networks
## 1 Introduction  
With the development of space exploration and the evolution of future space information networks (SIN), erasure correcting codes have attracted considerable research interest to enhance the information transmission capacity under the extremely challenging space communication environments [1], which are characterized by the frequent and lengthy link disruptions, high data loss and a long link delay [2]. In 2014, Consultative Committee for Space Data Systems (CCSDS) released an experimental specification of long erasure correcting (LEC) codes for near earth and deep-space communications [3], in which near-optimum fixed code rate Irregular-Repeat-Accumulate (IRA) codes are proposed. In [4], a joint design of the CCSDS file delivery protocol (CFDP) and IRA codes is discussed, and such erasure codes can be decoded efficiently with the Maximum-Likelihood algorithm [5], and the code rate can be selected from several values [6; 7]. Rateless codes (RC), also termed fountain codes, are capacity-achieving loss-resilient codes for erasure channels. Luby-Transform (LT) codes with a well-designed robust Soliton degree distribution (RSD) are the first practical realization of fountain codes [8]. They can recover the original \(k\) information (input) symbols from any \(N=k+O(\sqrt{k}\ln^{2}(k/\theta))\) received coded (output) symbols with probability \(1-\theta\) and the decoding cost of \(O(k\ln(k/\theta))\) operations, where \(\theta\) is the allowable failure probability to recover the original message after \(N\) coded symbols have been received. To further reduce the decoding complexity and to address the issue of high error floor in LT codes, [PERSON] proposed Raptor codes that concatenate the LT code with a weakened robust Soliton degree distribution (WRSD)with a high-rate pre-code [9]. In [10; 11], LT codes are incorporated into the CFDP implementation, and both of the Packets Interleaving CCSDS File Delivery Protocol and the Loss-Tolerant File Delivery Protocol are able to resist channel erasures and can further reduce obvious overhead in CFDP. Moreover, the line of sight (LOS) link is often unavailable for the space exploration rovers communicating to the base station directly [12]. The space exploration rovers and relay satellites can form a typical multi-access relaying SIN, which has a dynamic time-varying property of multi-hop links [13]. For example, the data from disjoint rovers/explorers need to be collected at the base station through a periodic relaying satellite [14]. Therefore, rateless codes have been considered in increasingly complicated SIN to provide an efficient distributed transmission scheme [15]. The first distributed LT (DLT) codes is proposed in [16]. The degree distribution for the distributed sources is designed as a way of decomposing the standard RSD, which is suited for a pre-fixed number of source nodes communicating with a single destination via a relay. In [17], selective distributed LT (SDLT) code is proposed by applying the And-Or tree analysis and linear programming, which can find some optimal combination at the relay node for an arbitrarily number of sources. In [18], soliton-like rateless coding (SLRC) scheme is designed for a Y-network, and SLRC scheme can provide degree distributions that generate LT-like output symbols in a relay with simple network coding protocol. It was shown through Monte Carlo simulations that the SLRC outperforms the DLT and SDLT. In [19], an improved approach of SLRC is proposed for the relay buffer-limited situation to ensure more effective decoding. The SIN is considered in the scenario that direct links and relay links are all existing, and an available degree distribution optimization scheme is proposed based on the And-Or tree analysis in [20]. The rateless network coding (NC) for dynamic relay topology based on [20] is investigated preliminarily for increasing the system throughput in this paper.