Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced stack decoding algorithm for PAC codes that significantly improves parallelization by exploiting specialized bit nodes, such as rate-0 and rate-1 nodes. For a rate-1 node with $N_0$ leaf nodes in its corresponding subtree, conventional stack decoding must either explore all $2^{N_0}$ paths, or, same as in fast list decoding, restrict attention to a constant number of candidate paths. In contrast, our approach introduces a pruning technique that removes candidate paths with small path metrics while ensuring that the probability of pruning the correct path decays exponentially with the threshold. Furthermore, we propose a novel approximation method for estimating variance polarization under the binary-input additive white Gaussian noise (BI-AWGN) channel. Leveraging these approximations, we develop an efficient stack-pruning strategy that selectively preserves decoding paths whose bit-metric values align with their expected means. This targeted pruning substantially reduces the number of active paths in the stack, thereby decreasing both decoding latency and computational complexity. Numerical results demonstrate that for a PAC$(128,64)$ code, our method achieves up to a 70\% reduction in the average number of paths without degrading error-correction performance.

翻译：极化调整卷积（PAC）码近年来作为一类有前景的纠错码涌现，特别是在短码长区域实现了接近容量性能。本文提出一种增强型PAC码堆栈译码算法，通过利用特定比特节点（如速率为0和速率为1的节点）显著提升并行化处理能力。对于子树中包含$N_0$个叶节点的速率为1节点，传统堆栈译码必须探索全部$2^{N_0}$条路径，或如快速列表译码般仅关注固定数量的候选路径。与此不同，我们的方法引入一种剪枝技术，在移除低路径度量候选路径的同时，保证正确路径被剪枝的概率随阈值呈指数衰减。此外，我们提出一种新的近似方法，用于估计二进制输入加性高斯白噪声（BI-AWGN）信道下的方差极化。基于这些近似，我们开发了一种高效的堆栈剪枝策略，选择性地保留比特度量值与其预期均值一致的译码路径。这种定向剪枝显著减少了堆栈中的活跃路径数量，从而降低了译码延迟和计算复杂度。数值结果表明，对于PAC$(128,64)$码，本方法在保持纠错性能不下降的前提下，平均路径数量最多可减少70%。