# Analytical Model and Feedback Predictor Optimization for Combined Early-HARQ and HARQ
## 3 Experimental Analysis  
### Link-Level Simulation Setup  
We perform experimental analysis with the transition probabilities, i.e., \(b_{1}(l)\), \(b_{2}(l)\) and \(b_{3}(l)\) extracted from 5G-compliant Link-Level Simulations (LLS). The simulation parameters are summarized in Table 2. A packet of 500 bits have been encoded using 5G-compliant LDPC codes and mapped to an 1.08 MHz OFDM transmission using a 64-QAM modulation. The encoded signal has been sent over a TDL-C fading channel and processed at the receiver using frequency domain MMSE and an LDPC min-sum decoder. We use a logistic regressions (LR) predictor as an e-HARQ mechanism, where the log-odds of a binary output variable are modelled as a linear combination of the classifier's input variable [21]. At smaller \(b_{1}(l)\) LR predictor operates more conservatively with sending ACKs whereas at  
Figure 4: Block diagram of a considered communication system on a high-level perspective.  
high \(b_{1}(l)\) it results in the increase of FP probability. Monte-Carlo simulations with 1.7 M iterations have been performed to estimate the probabilities, as described below. We varied the SNR between 5 dB and 12 dB and considered various subcode lengths between 1/2 and 5/6. The transition probabilities have been approximated as  
\[b_{2}(l)=P(\mathrm{rFB}_{l}=\mathrm{ACK}|\mathrm{eFB}_{l}=\mathrm{ ACK},\mathrm{rFB}_{l-1}=\mathrm{NACK})\\ \approx 1-\frac{P(\mathrm{rFB}_{l}=\mathrm{NACK}|\mathrm{eFB}_{l}= \mathrm{ACK})}{P(\mathrm{rFB}_{l-1}=\mathrm{NACK}|\mathrm{eFB}_{l-1}=\mathrm{ ACK})}, \tag{38}\]  
\[b_{3}(l)=P(\mathrm{rFB}_{l}=\mathrm{ACK}|\mathrm{eFB}_{l}=\mathrm{NACK },\mathrm{rFB}_{l-1}=\mathrm{NACK})\\ \approx 1-\frac{P(\mathrm{rFB}_{l}=\mathrm{NACK}|\mathrm{eFB}_{l}= \mathrm{NACK})}{P(\mathrm{rFB}_{l-1}=\mathrm{NACK}|\mathrm{eFB}_{l-1}=\mathrm{ NACK})}\,. \tag{39}\]  
The \(b_{1}(l)\) values have been initialized to the corresponding decoding probabilities for \(\theta=0\) defined as  
\[b_{1}(l):=P(\mathrm{rFB}_{l}=\mathrm{ACK}|\mathrm{rFB}_{l-1}=\mathrm{NACK}), \tag{40}\]  
and have been increased by a step size of 0.1 for each \(l\), respectively. Furthermore, the transition probabilities \(b_{1}(l)\) have been capped at 1. Therefore, resulting to \(b_{1}(l)=1\) for all \(l\) values at threshold \(\theta=9\).  
Figure 5 demonstrates an example of transition probabilities extracted from 5G-compliant link-level simulations with SNR = 10 dB and a packet transmission length of 14 OFDM symbols, which we further utilize to check the accuracy of the analytical model in Section 3.2. The plots show the curves for the first transmission only and encompass behavior for all subcode lengths: \(d=\overline{0,12}\) used for e-HARQ prediction. The threshold values \(\theta\) correspond to the monotonous increase from 0 to 1 in terms of \(b_{1}\), where 0 corresponds to permanent NACK generated by e-HARQ prediction, and 1--no prediction at all. When performing prediction based on a larger subcode length, i.e., \(d=12\), we can see that \(b_{1}\) rises, starting from 0.5 due to its higher accuracy and the given quality of the channel.  
Figure 5: Transition probabilities extracted from the 5G-compliant link-level simulations.