Motivated by the need to communicate short control messages in 5G and beyond, this paper carefully designs codes for cyclic redundancy check (CRC)-aided list decoding of tail-biting convolutional codes (TBCCs) and polar codes. Both codes send a 32-bit message using an 11-bit CRC and 512 transmitted bits. We aim to provide a careful, fair comparison of the error performance and decoding complexity of polar and TBCC techniques for a specific case. Specifically, a TBCC is designed to match the rate of a (512, 43) polar code, and optimal 11-bit CRCs for both codes are designed. The paper examines the distance spectra of the polar and TBCC codes, illuminating the different distance structures for the two code types. We consider both adaptive and non-adaptive CRC-aided list decoding schemes. For polar codes, an adaptive decoder must start with a larger list size to avoid an error floor. For rate-32/512 codes with an 11-bit CRC, the optimized CRC-TBCC design achieves a lower total failure rate than the optimized CRC-polar design. Simulations showed that the optimized CRC-TBCC design achieved significantly higher throughput than the optimized CRC-polar design, so that the TBCC solution achieved a lower total failure rate while requiring less computational complexity.

翻译：面向5G及未来通信中短控制消息的传输需求，本文精心设计了循环冗余校验（CRC）辅助的咬尾卷积码（TBCC）与极化码列表译码方案。两种方案均采用11位CRC校验码对32位消息进行编码，并占用512个传输比特。我们旨在针对特定场景，对极化码与TBCC技术的错误性能与译码复杂度进行严谨公平的对比。具体而言，设计了与(512,43)极化码速率匹配的TBCC，并分别为两种码字设计了最优11位CRC校验码。本文通过分析极化码与TBCC的距离谱，揭示了两种码型在距离结构上的差异。我们同时考虑了自适应与非自适应CRC辅助列表译码方案：对于极化码，自适应译码器需采用更大的初始列表规模以避免错误平层。对于采用11位CRC的速率32/512码字，优化后的CRC-TBCC方案相比优化后的CRC-极化方案具有更低的总失败率。仿真结果表明，优化后的CRC-TBCC方案在吞吐量上显著优于优化后的CRC-极化方案，因此TBCC方案能以更低的计算复杂度实现更低的总失败率。