# Adaptive Rate-Compatible Non-Binary LDPC Coding Scheme for the B5G Mobile System
## 1 Introduction
The communication system using the RC-LDPC code can adjust the code rate according to the current channel condition, so that the communication system can improve the transmission efficiency while satisfying the transmission reliability. In 2002, [PERSON] and [PERSON] combined the puncturing and extension methods to generate a series of RC-LDPC codes, which expanded the range of dynamic code rates [23]. In 2006, [PERSON] selected the location of the puncturing variable node from the perspective of the recovery tree, and proposed a grouping/sorting algorithm to sort the variable nodes according to the size of the recovery tree. The node with the smallest number of layers is used as the puncturing node [24]. In 2007, [PERSON] proposed another perforation measure [25]. The non-greedy criterion puncturing algorithm proposed in [26] shows better performance than the recovery tree-based puncturing algorithm. In [27], the shortening priority of variable nodes is divided according the column weight of each column in the check matrix, and a shortening algorithm suitable for whether irregular or regular quasi-cyclic LDPC codes was proposed. The traditional ACM technology selects the corresponding modulation and coding schemes according to the threshold calculated by the CSI fed back from the receiver, which depends largely on the assumed channel model [28; 29]. In fact, the real channel is not Gaussian-distributed; the amplifier incurs nonlinear effects, etc. Using the traditional ACM algorithm, it is often difficult to meet the frame error rate (FER) requirement [12; 30]. With the rise of machine learning algorithms, more simple and effective methods are used to reduce the complexity of the traditional methods [6; 31; 32]. The clustering algorithm is an important unsupervised learning algorithm in machine learning. Due to its flexibility, it is widely used in various technical fields [33; 34]. This paper studies an adaptive coding scheme for the B5G mobile system. We first develop a class of RC-NB-LDPC codes based on masking and puncturing techniques to construct the RC-LDPC codes. The masking technique converts the check matrix of the regular non-binary LDPC (NB-LDPC) code into one of irregular NB-LDPC code, and the puncturing technology constructs RC-NB-LDPC code. Then, we design a rate allocation scheme. Different from the existing works, we propose using the k-means++ clustering algorithm to cluster different channel environments, considering various factors that affect channel characteristics. This method relies on a perfect mathematical model and can learn interactively in the wireless channel. According to the actual error rate performance of the system, the correspondence between the signal-to-noise ratio and the modulation and coding mode is determined, which helps to select a more accurate coding rate. Finally, in order to present the advantages of the adaptive coding scheme in compressed image processing, we construct a coding scheme for image transmission. The numerical results demonstrate that the developed code can obtain better waterfall performance in a larger code rate range, which is more suitable for data transmission; the adaptive coding transmission scheme can obtain higher reconstructed image quality compared to the fixed code rate-coding scheme. Moreover, when considering UEP, the proposed scheme can further improve the reconstructed image quality. The remainder of this paper is organized as follows. The construction method and notations of RC-NB-LDPC codes are described in Section 2. In Section 3, we propose using the channel-clustering algorithm to cluster different channel parameters. In Section 4, we discuss the BER performance and decoding thresholds of RC-NB-LDPC codes. We also construct an adaptive coding scheme for image transmission to evaluate the performance of reconstructed image quality. We present our conclusions in the final section.