# Energy Efficient Communications for Reliable IoT Multicast 5G/Satellite Services
## 3 Network Coding  
The Network Coding (NC) approach, starting from the work of [PERSON] et al. [16] for wired networks, has recently gained more attraction in wireless terrestrial networks [17; 18; 19; 20] and can be a key enabling technology for 5G/satellite, mainly for reliable multicast services. NC techniques applied to satellite networks allow: (1) reducing the overall capacity needed to transfer data between peers, saving bandwidth in forward link; and (2) increasing network robustness in the case of residual packet erasures after the channel coding operations performed at the physical layer. As satellites commonly support simultaneous transmissions of the same packets toward a subset of nodes within the whole network, NC schemes further improve reliable multicasting. In the basic concept, NC allows the intermediate node (e.g., relay node) between the source and the destinations to process the received packets and send a linear combinations of them (generally a XOR operation). Packets are linearly encoded with coefficients chosen independently and randomly belonging to a Galois field of size \(q\). The destination nodes can decode them only if enough independent packets have been received, according to the random linear network coding (RLNC) concept. To apply this two-way relay NCtechnique to satellite network, we can consider an hub station and a satellite with a bent-pipe payload, or directly a satellite with a regenerative payload, to perform the XOR combining of previously received packets, for example sent by two terrestrial terminals. Each Earth terminal receives the XOR combined packet and can process it with its own stored packet to retrieve the packet transmitted by the other terminal, as shown in Figure 1a. The advantages are in terms of lower delivery delay and decreasing of bandwidth utilization (up to 50 % if NC is performed on board satellite). In this case, NC improves applications of videoconference between two satellite terminals or the use of satellite backhauling in geographical remote regions. For reliable multicast communications, the data are segmented and transmitted by an Earth station to the end terminals through satellite. Each terminal sends an acknowledgment (or negative acknowledgment) message if it has received correctly or not the packet, as in Figure 1b. NC is performed on board satellite providing redundancy in the packets to allow each multicast terminal to decode the missed packets. In Figure 1c, another transmission scheme is shown that does not require any acknowledgment message, thus minimizing the delivery delay, which usually represents a heavy constraint for reliable multicast services. As further explained, this is the assumption we made in deriving our system model. To this purpose, as explained in Section 4, we adopt the analytical derivation recently proposed in [21], which simplifies the one in [22], characterizing the exact decoding probability that the receiver node obtains \(N\) linearly independent coded packets among \(K(K\geq N)\) received coded packets. In the literature, the advantages of NC for reliable multicast communications via satellite are widely analyzed and a specific RFC has been also proposed by IETF [23]. The benefits of adoption of NC for content delivery in DVB-SH systems for handheld terminals without return link and for DVB-S2/RCS systems with fixed and mobile terminals, are highlighted in [24]. NC multicast is also analyzed in [25] for multibeam satellite system, where receivers can tune different frequencies or  
Figure 1: NC satellite communications schemes. polarizations to simultaneously decode orthogonal transmissions from adjacent beams and NC is used to enable decoding of signals from adjacent beams (spatial diversity). Besides, the performance of NCed satellite communications connecting two remote clusters on the Earth is analyzed in [8], by defining an optimization procedure to minimize the data flow delivery delay.