New algorithms for efficient decoding of polar codes (which may be CRC-augmented), transmitted over either a binary erasure channel (BEC) or an additive white Gaussian noise channel (AWGNC), are presented. We start by presenting a new efficient exact maximum likelihood decoding algorithm for the BEC based on inactivation decoding and analyze its computational complexity. This algorithm applies a matrix triangulation process on a sparse polar code parity check matrix, followed by solving a small size linear system over GF(2). We then consider efficient decoding of polar codes, transmitted over the AWGNC. The algorithm applies CRC-aided belief propagation list (CBPL) decoding, followed by ordered statistics decoding (OSD) of low order. Even when the reprocessing order of the OSD is as low as one, the new decoder is shown to significantly improve on plain CBPL. To implement the OSD efficiently, we adapt the matrix triangulation algorithm from the BEC case. We also indicate how the decoding algorithms can be implemented in parallel for low latency decoding. Numerical simulations are used to evaluate the performance and computational complexity of the new algorithms.

翻译：演示了高效解码极地代码(可能是CRC- 增强的)的新算法,该算法是通过二进制消化信道(BEC)或添加白高素噪声频道(AWGNC)传输的。我们首先展示了一种新的高效的极地代码加密新算法(CCRC-增强),其依据是非活化解码和分析其计算复杂性。这个算法对稀疏极地代码等同检查矩阵应用了矩阵三角程序,随后解决了GF(2)的小型线性系统。我们接着考虑通过AWGNC传输的极地代码的高效解码。该算法应用了CRC辅助的信仰传播列表(CBPL)解码,随后是低顺序的定序解码统计(OSD)。即使OSD的后处理顺序很低,但新的解码器显示在普通的CBPPOL上显著改进了。为了高效地执行OSD,我们从BEC案例中调整了矩阵三角算法。我们还指出了解码算法如何平行地执行低粘性解算法。