In order to solve the problem of high energy consumption of relay communication and high difficulty in the construction of 5G base stations, the research on Reconfigurable Intelligent Surface (RIS) technology was introduced in 6G mobile communication. Aiming at the problem of characteristic loss and instability of the truncated Hadamard matrix and Discrete Fourier Transform (DFT) matrix when constructing intelligent surfaces, a new RIS phase shift model design scheme of constructing unitary matrix based on Hankel matrix and Toeplitz matrix was proposed. The characteristics of the unitary matrix were used to minimize the channel error and improve the reliability of the communication channel. The simulation results show that compared with that of non-RIS-assisted communication, the user receiving rate of RIS-assisted communication can obtain a gain of 1 (bit·s ^-1)/Hz when the number of RIS units is 15. With the increase of the number of RIS units, the gain of the user receiving rate will be more and more significant. When the number of RIS units is 4, compared to the method of using DFT matrix to construct intelligent reflecting surfaces, the methods of using the two obtained unitary matrices to construct reflecting surfaces have higher reliability, and can obtain the performance gain of about 0.5 dB.

In order to improve the error code performance of Low Density Parity Check (LDPC) code Offset Min-Sum (OMS) algorithm, a low complexity OMS algorithm for 5G LDPC codes was proposed based on 5G NR standard. Aiming at the problem that the offset factor value calculation in the traditional algorithm is not accurate enough, the density evolution was used to obtain a more accurate offset factor value, which was used to the check node updating in order to enhance the performance of OMS algorithm. And the obtained offset factor value was approximated by using the linear approximation method, so as to reduce the complexity of the algorithm while ensuring decoding performance. For the influence of the variable node oscillation phenomenon on the decoding, the Log-Likelihood Ratio (LLR) message values before and after node updating were weighted, so the oscillation of the variable node was reduced, and the convergence speed of the decoder was improved. The simulation results show that compared with Normalized-Min-Sum (NMS) algorithm and OMS algorithm, the proposed algorithm improves the decoding performance by 0.3-0.5 dB when the Bit-Error Rate (BER) is 10 ^-5, and the average iteration times reduced by 48.1% and 24.3% respectively. At the same time, the difference between the performance of the proposed algorithm and LLR-BP (Log-Likelihood Ratio-Belief Propagation) algorithm performance is only nearly 0.1 dB.