This work identifies information-theoretic quantities that are closely related to the required list size for successive cancellation list (SCL) decoding to implement maximum-likelihood decoding. It also provides an approximation for these quantities that can be computed efficiently for very long codes. There is a concentration around the mean of the logarithm of the required list size for sufficiently large block lengths. We further provide a simple method to estimate the mean via density evolution for the binary erasure channel (BEC). Simulation results for the binary-input additive white Gaussian noise channel as well as the BEC demonstrate the accuracy of the mean estimate. A modified Reed-Muller code with dynamic frozen bits performs very close to the random coding union (RCU) bound down to the block error rate of $10^{-5}$ under SCL decoding with list size $L=128$ when the block length is $N=128$. The analysis shows how to modify the design to improve the performance when a more practical list size, e.g., $L=32$, is adopted while keeping the performance with $L=128$ unchanged. For the block length of $N=512$, a design performing within $0.4$ dB from the RCU bound down to the block error rate of $10^{-6}$ under an SCL decoder with list size $L=1024$ is provided. The design is modified using the new guidelines so that the performance improves with practical list sizes, e.g., $L\in\{8,32,128\}$, outperforming 5G designs.

翻译：这项工作确定了与连续取消列表(SCL)解码以实施最大类似值解码所需的列表大小密切相关的信息理论数量。 它还为这些数量提供了一个近似值,可以在非常长的代码中有效计算这些数量。 在足够大块长度的情况下,在所需的列表大小对数值的对数平均值周围有一个集中点。 我们还提供了一种简单的方法来通过密度变化来估计二进制淘汰通道(BEC)的平均值。 用于二进制添加白高尔西亚噪声频道和BEC的模拟结果显示了平均估算的准确性。 经过修改的Reed-Muller 代码与动态冻结比特的随机编码联盟(RCU)非常接近。 在 SCL 解码中, 以 $=518美元为单位。 当块长度为$=128美元时,我们提供了一种简单的方法来估计其平均值。 当更实用的列表大小,例如, $L=32美元, 美元, 和动态冻结比值的Reed-Muler 代码非常接近随机编码, 10-L=xxxxxxx 设计, 10x dxxx dx dx dx dxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx