论文标题
关于自动形态合奏解码的部分对称代码的分布
On the Distribution of Partially Symmetric Codes for Automorphism Ensemble Decoding
论文作者
论文摘要
自动形态集合（AE）解码最近引起了人们的注意，作为列出极地代码解码的替代方法。在这封信中，我们研究了部分对称的芦苇 - 毛刺（PS-RM）代码的分布，这是一个极性代码的家族，在AE解码下产生了良好的性能。我们证明，对于代码长度$ n \ leq 256 $的几乎所有代码维度的这些代码的存在。此外，我们分析了SC解码下的该代码家族的吸收组，证明了AE解码中的有价值排列始终存在。最后，我们通过实验表明，PS-RM代码可以在短代码长度的错误校正性能方面胜过最先进的极性代码构建算法，同时减少解码延迟。
Automorphism Ensemble (AE) decoding has recently drawn attention as a possible alternative to list decoding of polar codes. In this letter, we investigate the distribution of Partially-Symmetric Reed-Muller (PS-RM) codes, a family of polar codes yielding good performances under AE decoding. We prove the existence of these codes for almost all code dimensions for code lengths $N\leq 256$. Moreover, we analyze the absorption group of this family of codes under SC decoding, proving that valuable permutations in AE decoding always exist. Finally, we experimentally show that PS-RM codes can outperform state-of-the-art polar-code-construction algorithms in terms of error-correction performance for short code lengths, while reducing decoding latency.
