In this work, we investigate the performance of polar codes with the assistance of feedback in communication systems. Although it is well known that feedback does not improve the capacity of memoryless channels, we show that the finite length performance of polar codes can be significantly improved as feedback enables genie-aided decoding and allows more flexible thresholds for the polar coding construction. To analyze the performance under the new construction, we then propose an accurate characterization of the distribution of the error event under the genie-aided successive cancellation (SC) decoding. This characterization can be also used to predict the performance of the standard SC decoding of polar codes with rates close to capacity.

翻译：本文研究了通信系统中引入反馈机制后极化码的性能表现。尽管反馈无法提升无记忆信道的信道容量已是公认结论，但我们发现反馈能通过启用"精灵辅助"解码并为极化码构造提供更灵活的阈值选择，从而显著改善极化码在有限码长下的性能。为分析新构造下的性能表现，我们进一步提出了精灵辅助连续消除（SC）解码下误码事件分布的精确刻画方法。该刻画方法同样适用于预测接近信道容量时标准SC解码极化码的性能表现。