In this paper, we introduce a novel rate-profile design based on search-constrained optimization techniques to assess the performance of polarization-adjusted convolutional (PAC) codes under Fano (sequential) decoding. The results demonstrate that the resulting PAC code offers much reduced computational complexity compared to a construction based on a conventional genetic algorithm without a performance loss in error-correction performance. As the fitness function of our algorithm, we propose an adaptive successive cancellation list decoding algorithm to determine the weight distribution of the rate profiles. The simulation results indicate that, for a PAC(256, 128) code, only 8% of the population requires that their fitness function be evaluated with a large list size. This represents an improvement of almost 92% over a conventional evolutionary algorithm. For a PAC(64, 32) code, this improvement is about 99%. We also plotted the performance of the high-rate PAC(128, 105) and PAC(64, 51) codes, and the results show that they exhibit superior performance compared to other algorithms.

翻译：本文提出一种基于搜索约束优化技术的新型速率分布设计方法，用于评估极化调整卷积（PAC）码在Fano（序列）译码下的性能。结果表明，相较于基于传统遗传算法的构造方案，所提PAC码在保持纠错性能无损的前提下，显著降低了计算复杂度。我们采用自适应连续消除列表译码算法作为适应度函数，用以确定速率分布的权重分布。仿真结果表明：对于PAC(256,128)码，仅需对8%的种群采用大列表尺寸进行适应度评估，相比传统进化算法实现了约92%的效率提升；对于PAC(64,32)码，该提升幅度约为99%。此外，我们还绘制了高码率PAC(128,105)和PAC(64,51)码的性能曲线，结果显示这两种码字相比其他算法具有更优性能。