Conventional decoding algorithms for polar codes strive to balance achievable performance and computational complexity in classical computing. While maximum likelihood (ML) decoding guarantees optimal performance, its NP-hard nature makes it impractical for real-world systems. In this letter, we propose a novel ML decoding architecture for polar codes based on the Grover adaptive search, a quantum exhaustive search algorithm. Unlike conventional studies, our approach, enabled by a newly formulated objective function, uniquely supports Gray-coded multi-level modulation without expanding the search space size compared to the classical ML decoding. Simulation results demonstrate that our proposed quantum decoding achieves ML performance while providing a pure quadratic speedup in query complexity.

翻译：传统极化码解码算法致力于在经典计算中平衡可达性能与计算复杂度。虽然最大似然解码能保证最优性能，但其NP难特性使其在实际系统中难以应用。本文提出一种基于Grover自适应搜索（一种量子穷举搜索算法）的新型极化码最大似然解码架构。与常规研究不同，我们的方法通过新构建的目标函数，独特地支持格雷编码的多电平调制，且相比经典最大似然解码无需扩大搜索空间规模。仿真结果表明，所提出的量子解码在实现最大似然性能的同时，在查询复杂度上提供了纯粹的二次加速。