Polar codes, developed on the foundation of Arikan's polarization kernel, represent a breakthrough in coding theory and have emerged as the state-of-the-art error-correction-code in short-to-medium block length regimes. Importantly, recent research has indicated that the reliability of polar codes can be further enhanced by substituting Arikan's kernel with a larger one, leading to a faster polarization. However, for short-to-medium block length regimes, the development of polar codes that effectively employ large kernel sizes has not yet been realized. In this paper, we explore a novel, non-linear generalization of polar codes with an expanded kernel size, which we call DeepPolar codes. Our results show that DeepPolar codes effectively utilize the benefits of larger kernel size, resulting in enhanced reliability compared to both the existing neural codes and conventional polar codes.

翻译：极化码基于Arikan极化核构建，是编码理论的重大突破，已成为中短码长领域最先进的纠错码。值得注意的是，近期研究表明，通过将Arikan核替换为更大尺寸的核可进一步提升极化码的可靠性，从而实现更快的极化。然而，在中短码长范围内，能够有效利用大核尺寸的极化码尚未实现。本文探索了一种具有扩展核尺寸的非线性极化码新型泛化结构，我们称之为DeepPolar码。实验结果表明，DeepPolar码能够有效利用大核尺寸的优势，相较于现有神经编码方案和传统极化码，其可靠性均得到显著提升。