In this paper, we propose a data-driven algorithm to design rate- and length-flexible polar codes. While the algorithm is very general, a particularly appealing use case is the design of codes for automorphism ensemble decoding (AED), a promising decoding algorithm for ultra-reliable low-latency communications (URLLC) and massive machine-type communications (mMTC) applications. To this end, theoretic results on nesting of symmetric polar codes are derived, which give hope in finding a fully nested, rate-compatible sequence suitable for AED. Using the proposed algorithms, such a flexible polar code design for automorphism ensemble successive cancellation (SC) decoding is constructed, outperforming existing code designs for AED and also the 5G polar code under cyclic redundancy check (CRC)-aided successive cancellation list (SCL) decoding.

翻译：本文提出一种数据驱动算法，用于设计码率与码长可灵活配置的极化码。该算法具有高度通用性，其特别具有吸引力的应用场景是为自同构集成解码（AED）设计编码方案——AED是超可靠低延迟通信（URLLC）与大规模机器类通信（mMTC）应用中极具前景的解码算法。为此，本文推导了对称极化码嵌套的理论结果，为寻找适用于AED的完全嵌套且码率兼容的序列提供了理论依据。基于所提算法，我们构建了适用于自同构集成逐次抵消（SC）解码的灵活极化码设计方案，其性能不仅优于现有AED编码设计，也超越了采用循环冗余校验（CRC）辅助的逐次抵消列表（SCL）解码的5G极化码。