In this work, we present a framework that explores the tradeoff between the undetected error rate (UER) and block error rate (BLER) of polar-like codes. It relies on a novel approximation for what we call codebook probability, which assumes an auxiliary distribution mimicking the dynamics of decoding algorithms with successive cancellation (SC) decoding schedule. Simulation results demonstrates that, in the case of SC list decoding, the proposed framework outperforms the state-of-art approximations of Forney's generalized decoding rule for polar-like codes with dynamic frozen bits. In addition, the proposed generalized decoding outperforms the CRC-concatenated polar codes significantly in both BLER and UER. Finally, we briefly discuss two potential applications of the approximated codebook probability: coded pilot-free channel estimation and bitwise soft-output decoding.

翻译：本文提出了一个探索类极化码未检测错误率（UER）与块错误率（BLER）之间权衡的框架。该框架基于一种新颖的码本概率近似方法，该方法假设存在一个辅助分布，用于模拟采用连续消除（SC）译码调度机制的译码算法动态。仿真结果表明，在SC列表译码场景下，所提框架在动态冻结比特类极化码的Forney广义译码规则近似中优于现有技术水平。此外，所提出的广义译码在BLER和UER两个指标上均显著优于CRC级联极化码。最后，我们简要讨论了该近似码本概率的两个潜在应用：无导频编码信道估计与比特级软输出译码。