We propose a two-dimensional modified min-sum algorithm for the LDPC codes in the fifth generation (5G) networks standard to approach the error performance of the sum-product algorithm (SPA). In the proposed decoding algorithm, we adopt a partial self-correction method followed by message amplification to improve the reliability of the variable-to-check (V2C) messages. To further approach the performance of the maximum likelihood decoding for 5G short LDPC codes, we propose an enhanced quasi-maximum likelihood (EQML) decoding method. The proposed decoding method performs multiple rounds of decoding tests once the first decoding attempt fails, where the decoder inputs of the selected unreliable variable nodes are modified in each decoding test. A novel node selection method based on the sign fluctuation of V2C messages is proposed for the EQML decoding method. We also present a partial pruning stopping (PPS) rule to reduce the decoding complexity by deactivating part of the decoding tests once a valid codeword is found. A lower bound on the error performance is also derived by using the semi-analytical method. Simulation results show that the EQML decoding method outperforms the SPA with the same decoding complexity and other QML decoding methods, and it approaches the Polyanskiy-Poor-Verdú bound within 0.4 dB.

中文翻译：

---

基于2D修正最小和算法的5G LDPC码增强拟最大似然解码

我们为第五代 (5G) 网络标准中的 LDPC 码提出了一种二维修改的最小和算法，以接近和积算法 (SPA) 的误差性能。在所提出的解码算法中，我们采用部分自校正方法，然后进行消息放大，以提高可变校验（V2C）消息的可靠性。为了进一步接近 5G 短 LDPC 码的最大似然解码性能，我们提出了一种增强的准最大似然 (EQML) 解码方法。一旦第一次解码尝试失败，所提出的解码方法执行多轮解码测试，其中在每次解码测试中修改所选不可靠变量节点的解码器输入。针对EQML解码方法，提出了一种新的基于V2C消息符号波动的节点选择方法。我们还提出了部分修剪停止 (PPS) 规则，通过在找到有效码字后停用部分解码测试来降低解码复杂性。误差性能的下限也是通过使用半解析方法推导出来的。仿真结果表明，在解码复杂度相同的情况下，EQML 解码方法优于 SPA 和其他 QML 解码方法，并且在 0.4 dB 内接近 Polyanskiy-Poor-Verdú 界限。