# Cooperative Admission Control with Network Coding in 5G Underlying D2D-Satellite Communication
## 2 System Model
#### Network Packet Framework  
The network coding framework previously considered in literature consists of the cellular links or cellular-D2D links during the broadcast of the missing packets from the base station. These techniques exploit the strength of multiple interfaces to enhance the potential of network coding. To illustrate cellular network coding (NC), consider the Figure 2. After receiving the packets, assume due to channel noise, the p1 packet is missing from device 1. p2 packet is missing by device 2, and the p3 packet is missing for the device 03. The packets are recovered by re-transmitting the packet in cellular. In this case, 03 re-transmission is required to recover the lost packets. However, using network coding packets can be recovered in two timeslots by transmitting p1\(\oplus\)p2 and p2\(\oplus\)p3. The transmission has been reduced from 3 to 2. We will exploit the strength of D2D to recover the lost data, as shown in Figure 3. The device 1 has a p1 missing packet, so device 2 will transmit the p1\(\oplus\)p3 packet via the D2D link, and similarly, the other device will transmit p1. The transmission has been reduced from 03 timeslots to 2 timeslots, increasing the network coding gain. Figure 2: Network coding (Cellular only). Consider the cooperative network coding supported by the D2D-satellite interface, which is also used in our model. Suppose the base station transmits 04 packets. p1 is missing from device 1, p2 is missing from device 2, and p3-p4 packets are missing from device 3. To recover the packets effectively, we will now use all the interfaces available to recover the packets. First, p1\(\oplus\)p2 is transmitted by device 3 via the D2D link over the uplink. Simultaneously, the p3\(\oplus\)p4 packet is transmitted via satellite link for devices 1 and 2. So the transmission reduced from the 4 to 1. In same timeslot, the base station sends p5, which will be received by the devices with already received all the packets in the first stage of transmission. The benefit is that p4 is now available with the devices for re-transmission in the next time slot via the D2D link, as shown in Figure 4.  
The example demonstrates that as multiple interfaces are used, then the strength of the network coding is increased to manifolds. Let \(p\) denotes total packets for \(R\) admitted users. \(\Pi_{r}\) set of packets received and \(\gamma_{n}\) is set of device that receive packets such that \(\Pi_{(t,n_{t})}=\frac{p}{\gamma_{n}}\) in \(n_{t}\) stage. The reception and re-transmission of the packets have been divide into 02 stages. All the packets in the \(X\) set are broadcast via a cellular link in the first stage. In the second stage, the random linear combination of the packets is re-transmitted based on the cooperative admission network codes. The benefit for two stages is that in the first stage, only cellular links operate and result in less energy utilization because the devices need not operate in all modes, avoiding wastage of power. Second, if there is no loss in first stage, then the D2D-satellite links remain close. The benefit is lower energy and lowers link budget cost. As the cost of satellite links is expensive, so it is utilized in the second stage when deemed essential. In the first stage, all the packets \(p\) are transmitted from the base station to R devices via a joint admission link to decrease the loss at the first  
Figure 4: Multiple Access Network Coding (MANC). Figure 3: Network coding (D2D only). stage. However, due to the scarcity of the resources and noise, few packets are lost during the first stage, with the loss factor defined as:  
\[prb\_loss\_p(i)=\log\left(\frac{l(i)}{\alpha(i)}\right). \tag{9}\]  
\(prb\_loss\_p(i)\) denotes the logarithm of real packet loss probability during the time slot\([i;i+1]\). \(l(i)\) is the number of of lost packets and \(\alpha(i)\) is the number of packets that arrive. After the first stage, the set of packets lost is named as deficient \(D\).