# LDPC Decoder Design Using Compensation Scheme of Group Comparison for 5G Communication Systems
## 1 Introduction  
The market for fifth-generation (5G) communication systems is rapidly growing. 5G technology requires low-power and low-cost hardware equipment support because it considers the application requirements of enhanced mobile broadband (eMBB) and massive machine-type communication (mMTC). Immediate applications, such as in telemedicine and autonomous driving, will require ultra-reliable and low-latency communication (URLLC) support. Additionally, the corresponding specifications of the polar code and low-density parity-check (LDPC) code were proposed in the 15 th edition of the 5G specification [1] published in 2018. The error correction capability is of great importance when considering the advances in these techniques. The LDPC code [2], which comprises a forced error-correcting capability and fully parallel decoding architecture, was proposed by [PERSON] in 1962. Currently, LDPC codes have been introduced in different communication standards, such as DVB-S2 [3], IEEE 802.11n [4], IEEE 802.16e [5], and 5G new-radio (NR). LDPC is valued by researchers because it has powerful error-correction capabilities that are extremely close to the Shannon limit. However, LDPC has been difficult to implement in previous generations due to the complex calculations. Subsequently, process technology has evolved, and LDPC has been discussed and recently applied to most of the popular 5G communication fields. The requirement to achieve a throughput of 10 Gb/s for the 5G NR standard will also be a significant challenge for LDPC implementation. With the evolution of technology production, LDPC has been widely used in various communication fields, such as IEEE802.16e, IEEE802.11n, and the NAND flash channels [6]. Today, many approximations exist for the sum-product algorithm originally used in the LDPC, such as simplified versions of the normalized min-sum algorithm (NMSA) [7], the offset min-sum algorithm (OMSA) [8], and the normalized probabilistic min-sum algorithm (NPMSA) [9]. These studies simplify the hardware area, reduce the complexity of routing, and speed up the overall operation speed. Despite these advantages, they are inevitably accompanied by a loss in the error correction capability. In this study, we propose a flexible compensation scheme based on the NPMSA to achieve hardware simplification and recovery error correction ability. Without derivation, the proposed method was roughly verified in [10] for the LDPC decoding under the NAND flash channels. The contributions of this paper are that we explore the proposed compensation scheme using a thorough algorithm derivation with simulations, a detailed architecture design, a prototyping chip verification, and comparisons among several LDPC decoder chips. Simulation results reveal that the proposed compensation scheme operates effectively in different applications. Regarding the hardware implementation of the LDPC decoder for 5G communication systems, we adopted layered decoding, which is suitable for high-parallelism operations to achieve high throughput. For reference, the study in [11] proposed a further effective means of improving decoding performance of an LDPC code by extending single-decoder decoding to parallel decoding with multiple sub-decoders. The remaining sections are organized as follows. In Section 2, the decoders for the LDPC and QC-LDPC codes are introduced. In Section 3, the fundamentals of decoding and algorithms are described. We determine the NPMSA used in the successive sections. In Section 4, we describe the characteristics of the first and second probabilistic minimum. Based on these characteristics, we introduce the proposed compensation scheme to recover the decoding capability and maintain hardware simplification. In Section 5, we describe the architecture of the LDPC code design for different matrices, using base graph 1 (BG 1) and base graph 2 (BG 2) in the 5G NR standard. The post-layout results and a comparison of this study with related studies is subsequently presented. Finally, Section 6 provides a conclusion to this paper.