Abstract: 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.

Key words: 5th-Generation (5G), Low Density Parity Check (LDPC) code, Offset-Min-Sum (OMS), Density Evolution (DE), oscillation, linear approximation

摘要： 为了提高低密度奇偶校验（LDPC）码偏移最小和（OMS）算法的误码性能，基于5G NR标准提出了一种5G LDPC码的低复杂度OMS算法。针对传统算法中偏移因子值计算不够准确问题，使用密度进化获取更加精准的偏移因子值，用于校验节点更新，以增强OMS算法的性能；并使用线性近似方法对获得的偏移因子值进行近似处理，在保证译码性能的情况下降低了算法的复杂度。针对变量节点振荡现象对译码的影响，将节点更新前后的对数似然比（LLR）消息值加权处理，削减变量节点的振荡性，提高了译码器收敛速度。仿真结果表明，与归一化最小和（NMS）算法和OMS算法相比，在误比特率（BER）为10^-5时所提算法译码性能可以获得0.3~0.5 dB的增益，平均迭代次数分别降低了48.1%和24.3%，同时与对数似然比-置信传播（LLR-BP）算法也只相差近0.1 dB。

关键词: 5G, 低密度奇偶校验码, 偏移最小和, 密度进化, 振荡性, 线性近似