This work identifies information-theoretic quantities that are closely related to the required list size on average for successive cancellation list (SCL) decoding to implement maximum-likelihood decoding over general binary memoryless symmetric (BMS) channels. It also provides upper and lower bounds for these quantities that can be computed efficiently for very long codes. For the binary erasure channel (BEC), we provide a simple method to estimate the mean accurately via density evolution. The analysis shows how to modify, e.g., Reed-Muller codes, to improve the performance when practical list sizes, e.g., L∈[8,1024]L\in {[{8, 1024}]} , are adopted. Exemplary constructions with block lengths N∈{128,512}N\in \{128,512\} outperform polar codes of 5G over the binary-input additive white Gaussian noise channel. It is further shown that there is a concentration around the mean of the logarithm of the required list size for sufficiently large block lengths, over discrete-output BMS channels. We provide the probability mass functions (p.m.f.s) of this logarithm, over the BEC, for a sequence of the modified RM codes with an increasing block length via simulations, which illustrate that the p.m.f.s concentrate around the estimated mean.

中文翻译：

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连续取消列表解码和Polar码设计的信息论视角


这项工作确定了与连续消除列表 (SCL) 解码所需的平均列表大小密切相关的信息论量，以在通用二进制无记忆对称 (BMS) 通道上实现最大似然解码。它还提供了这些数量的上限和下限，可以有效地计算很长的代码。对于二进制擦除通道（BEC），我们提供了一种简单的方法来通过密度演化准确估计平均值。该分析显示了当采用实际列表大小（例如，L∈[8,1024]L\in {[{8, 1024}]} 时，如何修改例如Reed-Muller 码以提高性能。块长度为 N∈{128,512}N\in \{128,512\} 的示例性结构在二进制输入加性高斯白噪声通道上优于 5G 的极性码。进一步表明，在离散输出 BMS 通道上，对于足够大的块长度，所需列表大小的对数平均值周围存在集中。我们通过模拟提供了 BEC 上该对数的概率质量函数 (pmfs)，用于修改后的 RM 代码序列，块长度不断增加，这表明 pmfs 集中在估计平均值附近。