# Efficient QC-LDPC Encoder for 5G New Radio
## 1 Introduction  
Low-density parity-check (LDPC) codes [1], which were first proposed by [PERSON] in the early 1960s and rediscovered by [PERSON] and [PERSON] [2] in 1996, have attracted widespread attention thanks to their remarkable error correction capabilities near the Shannon limit, with advancements in very large-scale integration (VLSI). Moreover, LDPC codes are among the most widely used types of forward error correction (FEC) codes in several communications standards such as the wireless local area network (WLAN, IEEE 802.11n), wireless radio access network (WRAN, IEEE 802.22), digital video broadcast (DVB), and the Advanced Television System Committee (ATSC). Recently, the fifth generation (5G) communication has been a hotspot of research and development [3]. More specially, LDPC codes play an important role in 5G communication and have been selected as the coding scheme for the 5G enhanced Mobile Broad Band (eMBB) data channel [4]. To support compatible rate and scalable data transmission, 3 rd Generation Partnership Project (3 GPP) has agreed to consider two rate-compatible base graphs, BG1 and BG2, for the channel coding [5]. Accordingly, several studies have been conducted on the 5G LDPC codes. In [6], a low-cost and flexible demonstration platform is designed and implemented to evaluate the real-time performance of LDPC over the air interface as defined by 5G New Radio (NR) specifications. An algebra-assisted method for constructing 5G LDPC codes is presented in [7]. Over recent years, research on LDPC codes has been focused on structured LDPC codes known as quasi-cyclic low-density parity-check (QC-LDPC) codes [8; 9; 10; 11; 12], which exhibit advantages over other types of LDPC codes with respect to the hardware implementations of encoding and decoding usingsimple shift registers and logic circuits. A low-complexity encoder can be realized by using QC-LDPC codes, due to the sparseness of the parity check matrix. However, it is not straightforward to encode with low complexity as LDPC codes are defined by their parity check matrix, and the generator matrix is generally unknown. Various approaches have been suggested to improve the hardware complexity of LDPC encoders [13; 14; 15; 16; 17; 18; 19; 20; 21]. One of the most conventional approaches is systematic encoding, in which the generator matrix is derived from the parity check matrix by exploiting Gaussian elimination. The main drawback related to this method is that the storage overhead is dramatically increased for large block sizes, which limits its practical applicability. The Richardson-Urbanke (RU) algorithm is a widely-used LDPC codes encoding scheme developed by [PERSON] and [PERSON] [13]. The underlying principle of the method is the transformation of the parity check matrix into an approximate lower triangular (ALT) form by using only row and column permutations, which preserves the sparseness of the matrix. This method suffers from a long critical path, which could make the LDPC encoder unsuitable for high throughput applications. To overcome the limitations of the previous approaches, the design proposed in this paper, which is referred to as a low-complexity high-throughput LDPC encoder architecture for the 5G standard, requires significantly less area and memory storage while maintaining a high throughput. This paper targets the design of low-complexity high-throughput QC-LDPC encoders for the 5G NR standard. In LDPC encoders, the memory and interconnecting blocks are considered as the major influencing factors of the overall area, delay, and power performance of the hardware design. Hence, the size of the read only memory (ROM) was decreased by storing the quantized value of the permutation information for each submatrix instead of the entire parity check matrix \(H\). The proposed architecture requires less matrix multiplications than the RU method, by exploiting the characteristics of the 5G NR base matrix.