# Analytical Model and Feedback Predictor Optimization for Combined Early-HARQ and HARQ
## 1 Introduction  
The Fifth Generation (5G) mobile networks hold enormous potential for innovations across vertical industries given its promised multi-Gbps speed, 1 ms latency, and massive connectivity. Among the three important use cases of 5G systems are: enhanced Mobile BroadBand (eMBB), massive Machine Type Communications (mMTC), and mission critical MTC (cMTC) [1], which include applications with Ultra-Reliable Low Latency Communication (URLLC) requirements with a target error rate of less than \(10^{-5}\) and 1 ms end-to-end latency [2]. The cMTC exemplary scenarios that can only be enabled by URLLC [1]: are factory automation through network controlled systems, autonomous roads, platooning, haptic communications and many others. Despite the huge potential, according to the most recent 5G standard (3 GPP Release-16 [3]) low latency and machine-type communication tasks are still in progress, which implies latency efficient and reliable protocols toward URLLC to be a relevant research topic. The researchers in [4] have performed a full-fledged, end-to-end measurement study on one of the first commercial 5G networks, focusing on network coverage, end-to end throughput and delay, according to which there is still a room for improvement, as the radio access network latency reduction between 4G and 5G networks is negligible: \(2.19\pm 0.36\) ms (5G) vs. \(2.6\pm 0.24\) ms (4G). Among the techniques standardized in 3 GPP Release-15 aimed at achieving the strict requirements of reliability and latency are 5G flexible numerology, downlink pre-emption and uplink configured grant transmission [5, 6]. Release 16 has brought a couple of new enhancements in physicallayer design for URLLC, including Physical Downlink Control Channel (PDCCH) monitoring capability enhancements, new compact downlink control information format, Hybrid Automatic Repeat reQuest (HARQ) acknowledgement enhancement within a slot, and others [3]. There is plenty of research work that approaches the URLLC communications by enhancing the User Equipment (UE) feedback HARQ mechanism [7], which is a physical level protocol that sends ACK respond to the transmitter in case of successful decode of a packet and NACK in case of an error [8]. Its main limitation is Round TripTime (RTT), which is known to be a time interval between two transmissions. A plenty of research has been done on RTT reduction [9; 10; 11; 12]. In [9], researchers suggest reducing the latency by performing short data transmissions that take one Orthogonal Frequency Division Multiplexing (OFDM) symbol period, which in its turn have imposed higher power and processing requirements on both the receiver and the transmitter. Another approach approved in Rel. 16 comprises autonomous transmission of redundant data required to meet the reliability target [10]. However, it might degrade the spectral efficiency by sending unnecessary retransmissions due to the processing and feedback delays. In [11] the optimal and sub-optimal resource allocations are derived for URLLC considering the reliabilities of both data and control channels. The authors, in [12], develop a scheme, which enables a better protection of the NACK signal and is based on the asymmetric feedback signal detection allowing up to one retransmission. An early HARQ (e-HARQ) prediction--is another approach that has gained much attention recently due to its RTT reduction capabilities since it allows providing the feedback on the decodability of the received signal ahead of the end of the actual transmission process. The prediction is commonly performed by estimating the Bit Error Rate (BER) computed from the Log-Likelihood Ratios (LLRs) of bits with further hard thresholding as classification algorithms [13; 14; 15]. The researchers in [13] propose a method for on-line estimation of the BER during a turbo decoding process, in which LLRs are modeled as a mixture of two Gaussian random variables, after which the estimators for the mean and variance of these distributions are derived.