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In order to ensure the reliability, stability and high transmission rate of fifth-generation mobile communication technology(5G), this paper proposes a hybrid check matrix construction algorithm based on iterative coding algorithm with linear coding complexity. Firstly, this paper improves the traditional iterative coding algorithm and makes it suitable for non-binary low density parity check(NB-LDPC) codes. Then it adopts backward iterative method to change the coding scheme and the structure of the check matrix so that the progressive edge growth(PEG) algorithm has a lower triangular structure and uses it as the base matrix. Finally, a QC-LDPC algorithm with a lower triangular structure is used to generate a cyclic shift matrix and a finite field coefficient matrix. At the same time, the effect of the short loop is eliminated, and an optimal check matrix is selected from the algorithm. Simulation results show that the non-binary LDPC code constructed by the hybrid construction algorithm not only has linear coding and storage complexity, but also has strong error correction capability.

In the wireless communication system, it is necessary to change the transmitted code word or code rate in real time according to the channel environment, designing and implementing rate compatible codes is of great practical significance. In allusion to the defects of algebraically constructed QC-LDPC codes algorithm and the time-varying characteristics of wireless channel, we propose an algorithm based on check matrix optimization puncturing technique to construct QC-LDPC codes in this paper. The algorithm selects a high rate matrix with excellent performance as the parent matrix, and then uses the backward node puncturing method to puncture the information bits in the code word from the last column of the check matrix by a multiple of the number of rows to obtain a low rate matrix. The simulation results show that the rate-compatible non-binary LDPC codes constructed by this algorithm not only reduces the complexity of hardware implementation, but also improves the error correction performance of the non-binary LDPC codes, realizes the rate-compatible coding at the same time, and improves the average effectiveness and reliability of the communication system.