# Low-Latency Short-Packet Transmission over a Large Spatial Scale
## 1 Introduction  
5G wireless communication systems and a series of perspectives on conceptualized 6G systems have emerged as powerful platforms for multiple use cases such as augmented/virtual reality (AR/VR), teleoperated surgery, and automatic driving [1, 2]. An enhanced ultrareliable and low-latency communication (URLLC) has been proposed to support more stringent requirements on reliability and latency to meet the demands of those services. Specifically, the envisioned 6G wireless network may require URLLC based on a \(10^{-10}\) packet loss probability and an over-the-air latency on the order of 0.1 ms [3, 4]. With latency at a submillisecond level, short-packet transmissions are necessary [5]. Therefore, we should consider finite-blocklength channel coding to ensure reliability in URLLC. For the finite-blocklength (FBL) regime, the authors of [6] formulated the maximal coding rate of FBC over additive white Gaussian noise (AWGN) channels. The coding rate analysis has been extended to other practical scenarios, e.g., multiple-antenna fading channels [7], multiple-antenna Rayleigh-fading channels [8], block-fading channels [9], and hybrid automatic repeat request (HARQ) [10]. Latency is not only due to the physical layer transmission discussed in the literature above, but is also caused by the queuing of data packets in the network layer [11]. With a cross-layer design of variable-length coding for a single link, we have also achieved extremely low-latency communications in [12]. Thecross-layer design for URLLC was also discussed in [13; 14]. The author of [13] minimized the power consumption with a reliability constraint by adopting a packet-dropping policy. In [14], the violation probabilities of the maximal delay and peak-age of information were given for URLLC. Nonterrestrial communications are also at the forefront of 6G technology research [15], in order to provide three-dimensional (3D) coverage by complementing on-the-ground infrastructures with aerial platforms, including satellites. For large-scale communication systems, the signal-to-noise ratio, which decays rapidly with distance, is a crucial factor that affects system performance. For this reason, relaying is essential to gain higher reliability. Relay communication began to attract researchers' attention from the classical work of [16]. Various relaying schemes, including fixed relaying, selection relaying, and incremental relaying, were first discussed by [PERSON], [PERSON], and [PERSON] in [17]. Different cooperative schemes between the direct link and the relay link were discussed under both amplify-and-forward (AF) or decode-and-forward (DF) modes in [18]. In [19], we extended the decode-and-cancel protocol proposed in our previous work [20] to cancel inter-relay interference (IRI) in the scheme CAO-SIR. In CAO-SIR, we achieved an equivalent parallel relay model for DF-based successive relaying since the interference is entirely canceled by delicately adjusting the transmission order of relay nodes. Recently, researchers have also investigated relaying under the finite-blocklength regime (FBL). The authors in [21] derived closed-form expressions for the coding rates of relay communications under the Nakagami-m fading channel in the finite-blocklength regime. In [22], the researchers studied the relaying throughput performance of the quasi-static Rayleigh channels under the finite-blocklength regime, optimized the optimal distance and blocklength for URLLC, and compared that to the infinite-blocklength regime (IBL). However, relaying communications over a long distance suffer from technical difficulties such as the deterioration of the signal-to-noise ratio caused by the long distance, the increased latency caused by the increased number of relays, and the unclear theoretical upper limit of the optimal delay caused by the speed of light. In [21; 22], large-scale communication was not taken into consideration, and the authors' model was based on a fixed resource allocation and relay deployment scheme.