论文标题
关于PAC代码的度量和计算
On the Metric and Computation of PAC Codes
论文作者
论文摘要
在本文中，我们平均提供了最佳的度量函数，这导致了显着较低的解码计算，同时保持了极化调整后的卷积（PAC）代码的优势。借助我们提出的度量函数，PAC代码的解码计算与常规卷积代码（CC）顺序解码相当。此外，仿真结果显示使用我们建议的度量函数时，低速率PAC代码的错误纠正性能有所改善。我们证明，选择两极分化的截止速率作为度量函数的偏置值降低了顺序解码器在错误路径中相对于错误的路径深度的概率。我们还证明，PAC代码计算的上限具有帕累托分布。我们的仿真结果也验证了这一点。此外，我们提出了一个缩放偏置过程和选择阈值间距的方法，用于搜索限制的顺序解码，从而实质上改善了解码器的平均计算。我们的结果表明，对于某些长度为128的代码，搜索限制的PAC代码可以在连续的撤销列表下的误差校正性能达到误差校正性能，其列表大小为64，CRC长度为11，计算较低的CRC长度为11。
In this paper, we present an optimal metric function on average, which leads to a significantly low decoding computation while maintaining the superiority of the polarization-adjusted convolutional (PAC) codes' error-correction performance. With our proposed metric function, the PAC codes' decoding computation is comparable to the conventional convolutional codes (CC) sequential decoding. Moreover, simulation results show an improvement in the low-rate PAC codes' error-correction performance when using our proposed metric function. We prove that choosing the polarized cutoff rate as the metric function's bias value reduces the probability of the sequential decoder advancing in the wrong path exponentially with respect to the wrong path depth. We also prove that the upper bound of the PAC codes' computation has a Pareto distribution; our simulation results also verify this. Furthermore, we present a scaling-bias procedure and a method of choosing threshold spacing for the search-limited sequential decoding that substantially improves the decoder's average computation. Our results show that for some codes with a length of 128, the search-limited PAC codes can achieve an error-correction performance close to the error-correction performance of the polar codes under successive cancellation list decoding with a list size of 64 and CRC length of 11 with a considerably lower computation.
