# Adaptive Rate-Compatible Non-Binary LDPC Coding Scheme for the B5G Mobile System
## 1 Introduction  
With the advent of the 5G communication era, the demand for wireless communication is still strong, and the increased spectrum and power resources are insufficient. Therefore, new transmission technology needs to be updated to achieve rapid growth of the wireless communication capacity [1, 2]. The B5G mobile system performs well in terms of wireless coverage and user experience. To overcome the challenge, one should improve the error-correcting, anti-jamming, and efficient transmission capabilities for B5G. Among the communication technologies for error correction and detection, channel coding can significantly improve the reliability of communication systems and ensure efficient transmission--this has become one of the focuses among the communication technologies [3, 4, 5, 6, 7, 8, 9]. In order to achieve significant improvements with key performance parameters, the channel-coding technique for B5G should have features such as large coding gain, low-complexity, low-latency, high-throughput, and flexible code parameters [10, 11]. The conventional single channel-coding schemes can hardly meet all of the requirements of B5G. The B5G system will select different channel-coding schemes for different scenarios and serves to meet the corresponding technical requirements. For the B5G mobile system, the channel-coding scheme for a high data rate is pursued; however, the wireless channel environment is time-varying and fading. High-data-rate signals are proneto inter-symbol interference (ISI) in frequency-selective fading channels, which affects the overall transmission performance of the system [12]. In order to improve the throughput of the system, the adaptive coding method is proposed [13]. This method dynamically adjusts the coding mode of the transmitted signal according to the channel state information (CSI) fed back from the receiving end, and then finds a balance between the transmission rate and the transmission reliability to improve the throughput of the system. The DVB-S2 standard adopts an adaptive coding modulation (ACM) scheme in which channel coding comprises LDPC codes [14; 15]. However, the parameters such as the code length and the rate of LDPC codes in the DVB-S2 standard are fixed, and LDPC codes of different parameters need to design corresponding check matrices, resulting in the consumption of hardware resources. LDPC codes are currently among the most promising coding techniques to achieve the channel capacities for a wide range of channels. LDPC codes were first proposed by [PERSON] in 1962 [16], and developed in the late 1990s [17; 18]. Since their rediscovery, a great deal of research has been conducted in design, construction, encoding, and decoding algorithms. Many LDPC codes have been adopted as standard codes for current and next-generation communication systems, such as wireless, optical, satellite, deep space, multi-media broadcast (MMB), digital video broadcast (DVB) systems [8; 9; 10], and so on. This rapid dominance of LDPC codes in applications is due to their capacity-approaching performance, and they can be achieved with practically implementable iterative decoding algorithms. However, further research is needed to better understand the structural properties and performance characteristics of these codes. QC-LDPC codes, a subclass of LDPC codes [11], can be efficiently encoded and decoded by shift register adder accumulator (SRAA) [19; 20] and semi-parallel decoding architectures [21; 22], respectively. Thus, QC-LDPC codes can greatly reduce the consumption of hardware resources, and solve the complicated problem of implementing the codec from a certain angle. Rate-compatible LDPC (RC-LDPC) codes are a special set of LDPC codes with different code rates. These LDPC codes have good performance at each rate and can be implemented using the same set of codecs.