# Soft Iterative Decoding Algorithms for Rateless Codes in Satellite Systems
## 1 Introduction  
The rateless code is designed to generate infinite length of parities for a given length of information word, \(k\), resulting in its code rate to be \(k/\infty\approx 0\). Because of this rateless characteristic, it is often called a fountain code, and parity bits can be transmitted until perfect recovery of information is achieved. This eventually leads to capacity-achieving performance without any channel state information (CSI) report, and thus it can be efficiently utilized in unidirectional services such as multi-casting and broadcasting services. A receiver in a heterogeneous channel condition can access the ongoing mutli-cast session at an arbitrary time and can receive the message until it recovers the information without any error. Luby proposed the first class of rateless codes; they were called Luby transform (LT) codes [1]. Later, raptor codes were proposed in order to compensate for the disadvantages of LT codes; the typical design of a raptor code concatenated an LT code with a low-density parity check (LDPC) code [2]. Due to this strong advantage of rateless codes, evolved multimedia broadcast multicast services (eMBMS) introduced in the third-generation partnership project (3 GPP) adopted forward error correction (FEC) schemes with rateless codes in the application layer [3]. Satellite systems are an effective means of providing MBMS, and thus utilizations of rateless codes have been considered to provide efficient satellite broadcasting services [4; 5; 6; 7]. For example, in order to overcome the heterogeneity of the receivers and reduce the number of retransmissions, the packet level FEC scheme using LT codes was incorporated in a satellite data broadcasting system in [4]. In addition, raptor codeswere investigated in combination with the digital video broadcasting via satellite (DVB-S) specification, which is one of the most popular standards for broadcasting satellite services (BSS) [5; 6]. A cross-layer design of LT codes and LDPC codes was attempted for satellite multimedia broadcasting and multi-cast services, and the optimum parameters were designed to improve throughput performance for satellite multimedia transmission [7]. Considering that satellite bandwidth is a very expensive resource, recent satellite systems are required to adopt spectrally efficient transmission schemes, such as high-order modulation schemes and capacity-limiting FEC schemes. In addition, adaptive resource utilization, which is often referred to as adaptive coding and modulation (ACM) is needed in order to counteract various channel impairments in the physical (PHY) layer aspects. These requirements were reflected in the recent standards for satellite broadcasting services, such as digital video broadcasting--second generation satellite (DVB-S2) and its extension (DVB-S2X). Adaptive usage of resources, i.e., ACM requires closer interaction between the medium access control (MAC) and the PHY layers for optimum resource allocation. The hybrid automatic repeat request (HARQ) is an example of a cross-layer approach, where end to end data reliability is provided through a combination of PHY, data link, and transport layers. Modern satellite communication and broadcasting standards specify LDPC codes as an FEC coding scheme, and LDPC codes are known to provide excellent decoding performance by virtue of soft iterative decoding [8]. Even though multiple code rates of LDPC codes are defined for utilization of ACM in the existing satellite standards such as DVB-S2 and DVB-S2X, LDPC codes do not have their own rate compatibilities, i.e, multiple code rates cannot be generated from a single mother code. For this reason they cannot be directly applied to HARQ schemes which require rate-compatible FEC schemes to process incremental redundancy operations. In this regard, combining a rateless code with the existing LDPC code can be a solution [6].