# Dual Threshold Self-Corrected Minimum Sum Algorithm for 5G LDPC Decoders
###### Abstract  
Fifth generation (5G) is a new generation mobile communication system developed for the growing demand for mobile communication. Channel coding is an indispensable part of most modern digital communication systems, for it can improve the transmission reliability and anti-interference. In order to meet the requirements of 5G communication, a dual threshold self-corrected minimum sum (DT-SCMS) algorithm for low-density parity-check (LDPC) decoders is proposed in this paper. Besides, an architecture of LDPC decoders is designed. By setting thresholds to judge the reliability of messages, the DT-SCMS algorithm erases unreliable messages, improving the decoding performance and efficiency. Simulation results show that the performance of DT-SCMS is better than that of SCMS. When the code rate is 1/3, the performance of DT-SCMS has been improved by 0.2 dB at the bit error rate of \(10^{-4}\) compared with SCMS. In terms of the convergence, when the code rate is 2/3, the number of iterations of DT-SCMS can be reduced by up to 20.46% compared with SCMS, and the average proportion of reduction is 18.68%. 5G; low-density parity-check codes; belief propagation; minimum sum algorithm; self-corrected minimum sum algorithm +
Footnote †: journal: Information  
nodes can produce improved performance with lower complexity [3]. However, the introduction of puncturing variable nodes will also bring some performance loss when decoding, so it is necessary to improve the existing decoding algorithms. The LDPC code is a type of error correction coding with strong error correction capability, which was first proposed by MIT's [PERSON] in the 1960s [5]. Since LDPC codes have the advantages of simple description, low decoding complexity, parallel implementation, flexible use, and low error floor, they are widely used in practical communication and data storage systems [6; 7; 8; 9]. The LDPC code did not attract people's attention when it was proposed by [PERSON] due to the hardware and computer conditions at that time. In the 1990s, [PERSON] and [PERSON] proved that LDPC codes had the performance of approximating the Shannon limit under the combination of iterative decoding with the belief propagation (BP) algorithm, since then LDPC codes have gradually become a hot topic in academic research [10]. The disadvantage of the BP algorithm is that the computational complexity is high and the performance is seriously degraded, especially when the message quantization bits are low. In 1999, [PERSON] proposed the minimum sum (MS) algorithm to simplify the calculation of check node messages [11], and then MS quickly became the most widely used decoding algorithm. However, duo to the simplification, the decoding performance has a large loss, as well as some hard-decision algorithms [12; 13; 14; 15]. Therefore, many new improved algorithms appeared [16], such as the performance improvement algorithms modified by MS [17; 18; 19; 20], the approximate simplified algorithms for the decoding function [21; 22; 23; 24], and the scheduling algorithms with improved decoding efficiency [25; 26; 27; 28; 29; 30]. Among them, the offset minimum sum (OMS) algorithm and the normalized minimum sum (NMS) algorithm proposed by [PERSON] et al. improved the performance limitedly. Although the function approximation algorithms have improved performance, they still increase the computational complexity. The scheduling algorithms can reduce the computational complexity, but will lose some performance. Besides, the self-corrected minimum sum (SCMS) algorithm proposed by [PERSON] et al. improves the decoding performance from the perspective of variable node messages and accelerates the convergence of decoding [31; 32; 33]. However, the SCMS algorithm does not perform well when the channel state is good, and cannot meet the requirements of high reliability and efficiency-oriented communication systems.