## 4 Analysis of the Experimental Results
### Comparison of MPC and Multi-Path Fronthaul with Duplication (MPD)  
The second experiment compares the performance of MPC to that of the baseline MPD, which replicates the same data stream across multiple fronthaul paths. In particular, the analysis evaluates how the probability of error is improved by either of these two schemes and what the impact on the latency is. In this experiment, the focus is on the URLLC service, particularly on the tactile interaction in which reliability with low latency are key aspects. The payload sizes of the tactile interaction are typically \(\leq\)256 bytes and the error probability requirement is \(10^{-5}\)[18]. Fixed UDP packets of a size of 120 bytes are injected in PDCP in every frame. The probability of error vs latency function is presented in Figure 8, where the probability of error is defined as the probability that the measured RTT latency exceeds a predefined latency deadline \(t\), mathematically expressed as: \(P(X>t)\). This probability of error represents the packet error rate due to the fact that some packets arrive late or never arrive due to factors such as buffer overflows, queueing, and so on. It can be seen that, for latency values less than 250 us, the performance of MPC and MPD is generally the same. However, as latency increases to higher than 250 us, MPC delivers a lower error probability. MPC can achieve a latency reduction of 73 us, with respect to MPD at the error probability of \(10^{-5}\). It is interesting to look specifically at the  
Figure 8: Probability of error vs latency function for multi-path fronthaul with erasure coding (MPC) with \(k=2\) and multi-path fronthaul with duplication (MPD). _The dashed line represents the maximum latency to be supported by the MAC–PHY split._  
Figure 7: Distribution of jitter on the fronthaul for different packet sizes. performance at the latency of 500 \(\upmu\)s, which is the maximum acceptable RTT latency on the fronthaul for the MAC-PHY split [14]. At this point, shown by the vertical black line in Figure 8, MPC clearly outperforms MPD and can achieve an error probability of \(10^{-5}\) at 288 \(\upmu\)s latency, leaving a margin of 212 \(\upmu\)s to the maximum allowed RTT. Therefore, MPC is set to benefit from both diversity and the splitting of packets into smaller blocks. With MPC reaching an error probability of \(10^{-5}\) at a lower latency than MPD, a larger gap to the maximum allowed RTT can be gained. This gain can be beneficial for fronthaul dimensioning by allowing the distance between the (CU + DU) and the RU entities to be increased. The fronthaul distance can be extended by \(\text{t}_{\text{gap}}/(\text{prop}_{\text{delay}}\times 2)\), where \(\text{t}_{\text{gap}}\) is the time gap to the maximum allowed RTT, \(\text{prop}_{\text{delay}}\) is the propagation delay in the Ethernet, which is 5 \(\upmu\)s per km [19] and 2 accounts for the round trip. In our setup, for example, given that \(\text{t}_{\text{gap}}=212\)\(\upmu\)s at an error probability of \(10^{-5}\) for MPC (see Figure 8), the fronthaul can be extended by 42.4 km. Now, the performance of multi-path fronthaul is evaluated by emulating the delay in the fronthaul transport. In our next experiment, a delay is added to the fronthaul path 2 to emulate traffic congestion. An additional delay on path 2 will clearly affect the delivery of important information since link 2 carries the information required for decoding data. To investigate whether the delay would affect the performance of MPC due to the waiting effect described in Section 2, the network delay is emulated by using \(NetEM\) to add a normal distribution delay of 100 \(\upmu\)s \(\pm\) 10 \(\upmu\)s. Figure 9 shows the probability of error as a function of the latency. It can be seen that MPD and MPC start with the same probability of error, but after latency exceeds 100 \(\upmu\)s, the performance of the two schemes alternates. However, MPD outperforms MPC at an error probability of \(10^{-5}\).