# Low-Complexity Multi-Size Circular-Shift Network for 5G New Radio LDPC Decoders
###### Abstract  
This paper presents a low-complexity multi-size circular-shift network (MCSN) structure for 5 th-generation (5G) New Radio (NR) quasi-cyclic low-density parity-check (QC-LDPC) decoders. In particular, a fine-coarse approach-based multi-size cyclic shift network, which decomposes the cyclic shift size into fine part and coarse part, is introduced. The proposed MCSN structure is composed of a pre-rotator performing the fine part of the cyclic shift, and a main rotator executing the coarse part of the cyclic shift. In addition, a forward routing circular-shift (FRCS) network, which is based on the barrel shifter and the forward routing process is presented. The proposed switch network is able to support all 51 different submatrix sizes as defined in the 5G NR standard through an efficient forward routing switch network and help reduce the hardware complexity using a cyclic shift size decomposition method. The proposed MCSN is analyzed, and indicates a substantial reduction in the hardware complexity. The experimental results on TSMC 65-nm CMOS technology show that the proposed MCSN structure for 5G NR LDPC decoder offers an area saving up to 56.75% compared to related works in the literature. 5G New Radio; decoder architectures; LDPC code; switch network +
Footnote †: journal: _Sensors_  
definition  
QC-LDPC code requires circular-shift network (CSN) because of its cyclic characteristic. However, a QC-LDPC decoder for emerging wireless communication systems must support multiple code rates, various block lengths, and different submatrix sizes. The QC-LDPC codes adopted by the WiMAX standard (IEEE 802.16e) [14] supports 19 different submatrix sizes with four distinct code rates and six different class codes (distinct distributions of the number of variable nodes per column of check nodes per row). The submatrix sizes vary from 24 to 96. In the 5G NR LDPC code specification, 51 different lifting sizes are defined, and there are eight different permutation matrix designs per base graph [4]. For this reason, the switch network between CNNs and VNUs should be reconfigurable to support any submatrix sizes defined in the standards of applications. A switch network with varying sizes is called a multi-size circular-shift network (MCSN). Over the past few years, various works have been introduced in order to improve the signal congestion and hardware complexity of the MCSN for QC-LDPC decoders [15; 16; 17; 18; 19]. Benes network [15], which is capable of routing any \(Z\times Z\) permutation where \(Z\) is a power of 2, is a widely used structure. Benes network has been proven to be an optimal non-blocking permutation network. The main drawback of this method is its long critical path and high complexity, which makes it less efficient for implementation with the large size of submatrixes. One of the simplest approaches is assigning a multiple-input multiplexer (MUX) to each output. A MUX is assigned to an output, and each MUX has as many inputs as the number of input data items of the MCSN. This method suffers from high complexity since very wide-input MUXs is required. To overcome the overhead incurred by wide-input MUXs, [PERSON] [16] proposed a pre-rotator structure, in which small pre-rotators reduce the input width of the MUXs considerably. Furthermore, many other structures have been presented such as: rotator-in-series (RIS) structure [17], rotator-in-parallel (RIP) structure [16; 18], and fine-coarse (FC) structure [19]. However, the switch network structures in [15; 16; 17; 18; 19] are not suitable for 5G NR LDPC decoders where the submatrix sizes cover a very wide range from 2 to 384. To overcome the limitations of those approaches, this paper considers the design of low-complexity multi-size circular-shift network for 5G NR LDPC decoders, which requires significantly low hardware complexity compared to the conventional architectures. To the best of our knowledge, this is the first work proposing a low-complexity MCSN for the 5G NR LDPC decoders in the literature.