Besides the main decoding methods for polar codes such as successive cancellation (SC) decoding, SC list decoding (SCL), and belief propagation (BP) decoding, list sphere decoding (LSD) is an alternative for short codes regarding its lower complexity. Though the improved LSD (ILSD) can achieve better performance than LSD by a synchronous determination scheme, its performance is still not satisfactory with an inappropriate code construction. Good polar code construction is to pick the K most reliable bits from N bits. However, existing polar construction methods are designed for SC or BP decoders. These construction methods might not be suitable for ILSD, which searches based on the Euclidean distance. In this paper, a linear-complexity channel-independent polar code construction method for ILSD is proposed to improve the performance. Considering the Hamming distance as the reliability for ILSD, the proposed method arranges more frozen bits in the early synchro sets and improves the evaluation of the paths at each decoding level. With linear complexity, this method is channel-independent, which is efficient for offline constructions. Numerical results show the proposed construction with low code rates outperforms the state-of-the-art by 2 dB with ILSD.

除了用于极性码的主要解码方法（例如，连续取消（SC）解码，SC列表解码（SCL）和置信传播（BP）解码）以外，列表球面解码（LSD）由于其较低的复杂性是短码的替代方法。尽管通过同步确定方案，改进的LSD（ILSD）可以获得比LSD更好的性能，但是在不适当的代码构造下，其性能仍然不能令人满意。良好的极性代码构造是从N中选择K个最可靠的位位。但是，现有的极坐标构造方法是为SC或BP解码器设计的。这些构造方法可能不适用于基于欧几里得距离进行搜索的ILSD。为了提高性能，本文提出了一种线性复杂度与信道无关的极性代码构造方法。考虑到汉明距离作为ILSD的可靠性，所提出的方法在早期同步集中安排了更多的冻结位，并改善了每个解码级别的路径评估。由于具有线性复杂度，因此该方法与通道无关，这对于离线构造非常有效。数值结果表明，采用ILSD时，建议的低码率结构优于最新结构2 dB。