常用的max-log-map与log-map算法相比降低了软信息计算复杂度，但对高阶正交幅度调制（QAM）资源消耗仍较大，如8QAM、16QAM概率整形（PS）和64QAM PS。

8QAM采用星座区域划分的方式，文章中，软信息采用接收符号到最近比特0与比特1中垂线的距离信息表示，利用角度旋转和区域对称性简化计算距离信息；非麦克斯韦玻尔兹曼（MB）分布的16QAM PS和64QAM PS，比特1所在区域两侧边缘之间的中心界线与区域两侧比特0之间的中心界线不再重合，对区域进行合并近似，处理两界线间区域归属，展开max-log-map算法因式简化距离差计算软信息；基于MB分布的16QAM PS和64QAM PS的软信息可由非MB分布的软信息表达式化简得到。

经上述简化后，与max-log-map算法相比，8QAM软信息计算乘法次数48次和加减法次数75次分别缩减为12和16次，解调性能仅退化约0.05 dB；MB分布的16QAM PS乘法次数192次和加减法次数260次分别缩减为2和4次，解调性能仅退化约0.05 dB；更高阶的64QAM PS资源消耗缩减程度更大，乘法次数1 152次和加减法次数1 542次分别缩减为3和6次。

文章提出了适用于8QAM、MB分布的16QAM PS、MB分布的64QAM PS、非MB分布的16QAM PS和非MB分布的64QAM PS 软信息计算方法。当概率满足MB分布时，非MB分布的软信息计算方法可转化为MB分布计算方法；当PS因子为0时，基于MB分布的表达式可转化为均匀分布软信息计算式，非MB分布、MB分布和均匀分布的软信息计算可使用同一电路统一设计，提高电路复用率，降低硬件资源消耗。

The commonly used max-log-map algorithm reduces the complexity of soft information computation compared to the log-map algorithm. However, it still consumes significant resources for high-order Orthogonal Amplitude Modulation (QAM), such as 8QAM, 16QAM Probability Shaping (PS), and 64QAM PS.

8QAM adopts the method of constellation region division, and the soft information is represented by the distance information from the received symbol to the perpendicular between the nearest bit 0 and bit 1. The distance information is simplified and calculated using angle rotation and regional symmetry. For 16QAM PS and 64QAM PS with non Maxwell Boltzmann (MB) distribution, the central boundary between the edges of the bit 1 region and the central boundary between bit 0 on both sides of the bit 1 region no longer coincide. Region merging approximation is used to handle the region ownership between the two boundaries, and the max-log-map expression is factorized to simplify the distance difference to calculate the soft information. The soft information of 16QAM PS and 64QAM PS based on MB distribution can be obtained by simplifying the soft information expression of non-MB distribution.

The simplification reduced the multiplication and addition/subtraction operations in 8QAM soft information calculation from 48 and 75 times to 12 and 16 times respectively. with a degradation of only about 0.05 dB. For MB-distributed 16QAM PS, operations reduce from 192 multiplications and 260 additions/subtractions to 2 and 4, respectively, also with a degradation of only about 0.05 dB. The reduction is even greater for 64QAM PS, decreasing from 1 152 multiplications and 1 542 additions/subtractions to 3 and 6, respectively.

This article proposes a soft information computation method suitable for 8QAM and MB-distributed 16QAM PS, MB-distributed 64QAM PS, non MB-distributed16QAM PS, and non MB-distributed 64QAM PS. When probabilities align with the MB distribution, the non MB methods can transform into the MB methods. When the shaping factor is 0, the expression based on the MB distribution can be converted into a uniformly distributed soft information calculation formula. The soft information calculation for non-MB distribution, MB distribution, and uniform distribution can be uniformly designed on the same circuit, improving circuit reuse rate and reducing the hardware resource consumption.