Polar codes with large kernels can achieve improved error exponents but are challenging to design with low decoding com- plexity. This work investigates kernel construction under recursive maximum likelihood decoding (RMLD) using a reinforcement learning framework based on the Gumbel AlphaZero algorithm. The proposed method efficiently explores the design space and identifies large-size kernels that satisfy a given error exponent while minimizing decoding complexity. For a size-16 kernel, it achieves 17% lower decoding complexity than handcrafted designs while reaching an error exponent of 0.5183 compared to 0.5 for Arikan's kernel, demonstrating the effectiveness of the learning-based approach for practical polar code construction.

翻译：采用大核的极化码能够获得更优的错误指数，但其低解码复杂度的设计颇具挑战。本研究基于Gumbel AlphaZero算法，利用强化学习框架，探索在递归最大似然解码（RMLD）下的核构造方法。所提出的方法能够高效探索设计空间，识别出满足给定错误指数且解码复杂度最小化的大尺寸核。对于尺寸为16的核，该方法相比手工设计实现了解码复杂度降低17%，同时达到0.5183的错误指数（Arikan核为0.5），验证了基于学习的方法在实际极化码构造中的有效性。