论文标题
列表Arikan PAC代码的解码
List Decoding of Arikan's PAC Codes
论文作者
论文摘要
极性编码产生了第一个明确的代码家族,该家族可通过有效的编码和解码为广泛的渠道实现容量。但是,它在短块长度上的性能远非最佳。阿里坎(Arikan)最近提出了一种新的极地编码方案,他称其为极化调整后的卷积(PAC)代码。与标准连续的策略解码以及CRC ADED列表解码相比,此类PAC代码可提供性能的显着改善。 Arikan的PAC代码主要基于以下思想:用卷积的预编码(在适当的速率分析)中代替CRC预编码,并通过顺序解码代替解码列表。他的模拟表明,PAC代码是由这些想法的组合产生的,几乎在ML解码下的任何代码的性能上都接近有限的长度范围。 本文中我们的主要目标之一是回答以下问题:顺序解码对于PAC代码的出色性能至关重要吗?我们表明,当列表尺寸$ l $中等大(例如$ l \ ge 128 $)时,可以使用列表解码实现类似的性能。列表解码比顺序解码具有不同的优势,例如某些情况,例如低SNR制度或最差的复杂性/潜伏期是主要约束的情况。另一个目的是提供一些对PAC代码的出色性能的见解。我们首先观察到,顺序解码和列表PAC代码的解码密切匹配ML解码。然后,我们使用这些估计值估算了PAC代码中低重量代码字的数量,以近似于其在ML解码下的性能上的结合。这些结果表明,PAC代码既优于极地代码和芦苇毛刺代码,又表明速率的目标可能是优化低权重时的重量分布。
Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short block lengths is far from optimal. Arikan has recently presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. Such PAC codes provide dramatic improvement in performance as compared to both standard successive-cancellation decoding as well as CRC-aided list decoding. Arikan's PAC codes are based primarily upon the following ideas: replacing CRC precoding with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. His simulations show that PAC codes, resulting from the combination of these ideas, are close to finite-length bounds on the performance of any code under ML decoding. One of our main goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size $L$ is moderately large (say, $L \ge 128$). List decoding has distinct advantages over sequential decoding is certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, using these estimates to approximate the union bound on their performance under ML decoding. These results indicate that PAC codes are superior to both polar codes and Reed-Muller codes, and suggest that the goal of rate-profiling may be to optimize the weight distribution at low weights.