# Sum of the Magnitude for Hard Decision Decoding Algorithm Based on Loop Update Detection  
[PERSON]  
1 College of Information & Communication Engineering, Harbin Engineering University, Harbin 150001, China; [EMAIL_ADDRESS] (D.Z. ); [EMAIL_ADDRESS] (H.T. ); [EMAIL_ADDRESS] (L.Z.) [PERSON]  
1 College of Information & Communication Engineering, Harbin Engineering University, Harbin 150001, China; [EMAIL_ADDRESS] (D.Z. ); [EMAIL_ADDRESS] (H.T. ); [EMAIL_ADDRESS] (L.Z.) [PERSON]  
1 College of Information &  
perspective of reducing the decoding complexity of the study [11], with the improved algorithm applied to 5G mobile communications in the human-centric high-speed communications. The representative algorithm in HDA is a bit-flipping (BF) algorithm [12], which has low complexity and computational complexity. The algorithm is simple and easy to implement in hardware, but the decoding performance is not as good as the SDA. Therefore, the HDA is mainly studied from the perspective of improving the decoding performance, with the improved algorithm applied to a machine-centric low-rate, low-latency system in 5G mobile communications. In the future, the 5G mobile communication system in 2020 will provide higher data transmission rate, more service connections and better user experience while ensuring low cost, transmission security, reliability and stability [13]. Channel coding in 5G mobile communication involves non-binary LDPC codes [14]. Although non-binary LDPC codes have excellent error correction performance, the complexity of high decoding is the main reason that restricts its practical application. Therefore, this paper optimizes the performance of the HDA with low complexity, and optimizes it using the symbol flipping (SF) algorithm. For the hard decision decoding algorithm, the weighting symbol flipping (WSF) algorithm proposed in literature [15] constructs a new flip function by using the minimum value of the variable node amplitude adjacent to the check node (CN) as the reliability of the check equation. On this basis, the reliability information of VN is used as the input of the flip function by the weighting factor and thus, the performance of the modified weighted symbol flipping (MWSF) algorithm will be improved [16]. Based on the belief propagation theory, the decoding algorithm proposed by literature [17] achieves a certain degree of coding gain. In this paper, this is called the improved MWSF (IMWSF) algorithm. Since then, there have been proposals of an average probability and stopping criterion weighted symbol flipping (APSCWSF) algorithm [18; 19], multiple-vote symbol flipping (MV-SF) algorithm [20; 21; 22] and so on [23; 24]. Current communication systems need to have faster and more efficient decoders than previous ones. On this basis, many scholars have studied the fast convergence and low complexity decoding algorithm with minimum decoding loss [25; 26; 27; 28]. For the WSF algorithm proposed in literature [19; 25], the destruction of the parity relation is attributed to the lowest reliability symbol in the check equation. However, if one check equation is not established, all the symbols involved in the equation may be wrong, but the symbols with lower reliability are more likely to be wrong. Therefore, a new calculation method of reliability is redefined in this paper. When calculating the reliability of variable nodes from each check equation, the reliability information of each variable node participating in the check is taken into account. Furthermore, the sum of the amplitudes of the variable nodes adjacent to the check node is used as the reliability of the check equation. At the same time, when calculating the reliability of participating check symbols, excluding the information carried by the symbol itself, a weighted symbol flipping decoding algorithm based on the magnitude sum (SMWSF) is proposed to obtain more effective soft information for reliability.