# 5G V2X Performance Comparison for Different Channel Coding Schemes and Propagation Models
## 1 Introduction and Literature Review  
Intelligent Transportation Systems (ITSs) represent efficient solutions for improving traffic safety and efficiency, as well as providing infotainment services. V2X communications include vehicle-to-vehicle (V2V), vehicle-to-network (V2N) or vehicle-to-infrastructure (V2I), vehicle-to-road side unit (V2R) and vehicle-to-pedestrian (V2P) communications, and they represent the key enablers of ITSs [1]. V2X communication helps vehicles to obtain and share information periodically (also known as beaconing), such as location, speed, braking action, road and intersection status, to improve safety. ITSs were introduced in 1999 by the US Federal Communication Commission, and they immediately triggered significant research activity all over the world and especially in the USA [2] and Europe [3]. The research resulted in a first set of radio standards for V2X in the USA [4] and in Europe [5], respectively. The first standard to present direct device-to-device (D2D) communications was 3 GPP Release 12, which was originally developed for safety services [6]. 3 GPP Release 12 introduced a new service function, the Proximity Service, which allows the devicesto discover peer devices for D2D communication services and to directly communicate and exchange data with neighbouring entities. This initiative served as the base for the development of LTE V2X based on the 4G LTE under Release 14 [7] and 15 [8]. 3 GPP Release 15 included 5G NR also, but it did not include sidelink aspects. Release 16 is the first to introduce V2X communications, including sidelink communications, based on the 5G NR air interface [9]. It focuses on enhancing V2X reliability, latency, capacity and flexibility and it also targets advanced use cases, such as platooning, extended sensors, advanced driving and remote driving [10]. All the above communication standards use the Forward Error Correction technique for controlling errors in data transmission over noisy communication channels. On the other hand, turbo codes, based on the turbo principle [11], represented a revolutionary channel coding signal processing technique, introduced in 1993 [12; 13], to achieve near Shannon performance [14]. The critical and most complex process is turbo decoding. Mainly, two decoding algorithms are used for turbo decoding. The MAP algorithm of [PERSON], Cocke, Jelinek and Raviv (BCJR) [15], and the Soft-Output Viterbi Algorithm (SOVA) [16], which though simpler, has some deprivation in performance. BCJR is a complex algorithm, so the less complex but suboptimal Max-Log-MAP implementation of the algorithm [17; 18] was proposed. Further, the Log-MAP implementation of the algorithm [19] was proposed, giving a performance close to that of the MAP algorithm and correcting the approximation used in the Max-Log-MAP. Turbo codes had superior performance, and due to their excellent error-correcting capability, they rapidly became part of 4G-LTE [20; 21], but latency and complexity were drawbacks, mainly due to large frame sizes [22]. LDPC [23; 24; 25] is much simpler [26] than turbo coding. According to 3 GPP TS 38.212 [27], LDPC is recommended for 5G NR shared channels due to its high throughput, low latency, low decoding complexity and rate compatibility [28; 29]. On the contrary, it does not perform very well for a short code length and low code rate [30]. Polar codes [31] are the first provably capacity-achieving family of codes with low encoding and decoding complexity. Due to the good performance [28; 29], polar codes are now being used to transmit control information in the 3 GPP 5G-NR [32]. In [33], the authors showed that turbo codes can be used for enhancing safety-related 5G V2V and V2I services for short frame lengths and correlated (flat) Rayleigh fading channel. In [34] and [35], the authors investigated the impact of turbo codes on the quality of service and BER performance, considering a 3 GPP 5G NR V2X environment and small length frames.