# An Efficient QC-LDPC Decoder Architecture for 5G-NR Wireless Communication Standards Targeting FPGA
## 1 Introduction  
Clear communication has always been hindered by the problem of unreliable or noisy channels, ever since telecommunication systems and information theory were developed. With the prevalence of cellular communication and the transmission of sensitive data, the problem has seen a significant rise [1]. [PERSON] invented the first Error Correction Code (ECC) in 1950 [2] to control and correct errors in data transmission over noisy channels. The encoding component of the ECC's error control procedure includes the addition of redundant information to address potential errors across the message. The decoding process automatically detects and corrects errors once the data are received. In the context of 5G, significant advancements have been made in the error correction process, as depicted (see Figure 1). This process involves CRC (Cyclic Redundancy Check) verification, where a short, fixed-size check-sum is initially computed based on the information packet. On the other hand, the CRC check recalculates this checksum and compares it to the one received to ensure data integrity. Block segmentation serves the purpose of splitting a longer data stream into smaller segments. Conversely, block concatenation involves combining smaller data blocks into a continuous stream. The rate matching/adaptation technique is employed to synchronize the data rates across various components of the system, ensuring efficient data transfer without overloading certain parts of the system. Bit interleaving involves merging bits from multiple source data streams into a unified stream, following a particular pattern. The BER and Signal-to-Noise Ratio (SNR) metrics are employed to characterize the decoding capabilities [3; 4]. The SNR is defined as the signal power divided by the noise power, whereas the BER is the number of errors divided by the total number of transmitted bits. The main contribution of coding theory is to achieve lower SNRs for the same BER [5; 6]. If an uncoded system has a BER of \(10^{-4}\) at an SNR level of 4 dB, the corresponding coded system should have the same BER at a lower SNR (3.5 dB). In this case, the coding gain is 0.5 dB, which will decrease the signal power for the same BER. After being long ignored, LDPC codes have become one of the major codes for contemporary standards, as in the second-generation satellite digital video broadcast (DVB-S2) and 5G-NR wireless communication [7; 8]. They were invented by [PERSON] at the beginning of the 1960s [9]. Recently, they have been adopted for use in many significant communication systems, such as the Consultative Committee for Space Data Systems (CCSDS) [10]. The min-sum algorithm, a foundational technique in iterative decoding for LDPC codes, was initially derived as a simplified approximation of the Belief Propagation (BP) algorithm. Its efficiency and relatively low computational complexity have made it a popular choice for practical implementations. Subsequent variants such as Offset Min-Sum (OMS) [11], Approximate Min-Sum (AMS) [12], and Scaling Min-Sum (SMS) [13] have been introduced to enhance performance by incorporating additional approximations. The OMS algorithm introduces an offset value to the message passing process, aiming to improve error floor performance. AMS simplifies the min-sum computations by using approximations, potentially reducing computational complexity. Finally, SMS applies scaling factors to the messages to enhance decoding performance. The authors in [11] proposed a fully parallel architecture built on the first base graph (BG1). The internal modules of this architecture are equipped with multiplexers that have been designed based on the columns of the base graph. This has led to 19 parallel 68:1 multiplexers, which may require additional resources as they are constructed based on columns instead of rows. Additionally, the circular shifting blocks in this architecture receive addresses from a ROM memory, which can limit its design flexibility based on the characteristics of the base graph.