[论文解读] List Decoding of Arikan's PAC Codes

Hanwen Yao, Arman Fazeli+1 more|May 27, 2020

Error Correcting Code Techniques被引用 8

一句话总结

该论文表明，当列表大小适中偏大时（例如，$L \geq 128$），列表译码在Aríkan的PAC码中可实现与串行译码相当的性能，从而挑战了PAC码优越性能必须依赖串行译码的必要性。作者表明，两种译码方法均能紧密逼近ML译码性能，并将PAC码的成功归因于通过码率配置优化的有利低权重码字分布。

ABSTRACT

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.

研究动机与目标

• 探究串行译码是否为PAC码优越性能所必需。
• 评估在PAC码中用列表译码替代串行译码的可行性与性能表现。
• 深入理解PAC码的权重分布及其在实现近似ML性能中的作用。
• 通过最小化低权重码字，为未来PAC码设计提供最优码率配置与预编码选择的指导。

提出的方法

• 作者通过将PAC码视为具有动态冻结比特的极化码，提出了一种PAC码的列表译码算法。
• 采用逐次消除列表译码，并使用足够大的列表大小（$L \geq 128$），以实现与串行译码相近的性能。
• 估算PAC码及其他相关码型（如极化码、Reed-Muller码）中的低权重码字数量，利用截断并集界近似ML译码性能。
• 比较不同码率配置（极化码与RM码配置）下PAC码的权重分布，分析其对性能的影响。
• 通过仿真与复杂度分析，对比列表译码与串行译码在最坏情况延迟与计算负载方面的表现。
• 使用Aríkan的串行译码源代码与数据进行基准测试与验证。

实验结果

研究问题

• RQ1 在PAC码中，列表译码能否实现与串行译码相当的性能？
• RQ2 PAC码的近似ML性能是否必须依赖串行译码？
• RQ3 PAC码的权重分布（尤其是低权重部分）如何影响其在ML译码下的性能表现？
• RQ4 码率配置在最小化低权重码字与提升码性能方面发挥何种作用？
• RQ5 在最坏情况复杂度与延迟方面，列表译码是否可作为串行译码的可行替代方案？

主要发现

• 当$ L \geq 128 $时，列表译码在PAC码中实现的性能与串行译码无明显差异，表明串行译码并非PAC码优越性能所必需。
• 采用RM码率配置的PAC码中，低权重码字数量显著低于Reed-Muller码，仅含3120个权重为16的码字，而Reed-Muller码则有94,488个。
• 采用RM码率配置的PAC码保持了16的最小距离，与自对偶Reed-Muller码一致，但最小权重码字数量减少了30倍。
• 基于估计权重分布的截断并集界能紧密逼近ML译码性能，验证了权重分布分析作为性能预测工具的有效性。
• 在列表译码与串行译码下，PAC码的性能均紧密逼近ML译码性能，表明通过高效译码可实现近似ML性能。
• 结果表明，最优码率配置应优先考虑最小化低权重码字，这是PAC码实现卓越性能的关键因素。