Recently, rate-$1/\omega$ zero-terminated and tail-biting convolutional codes (ZTCCs and TBCCs) with cyclic-redundancy-check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short blocklengths. This paper designs CRCs for rate-$(\omega-1)/\omega$ CCs with short blocklengths, considering both the ZT and TB cases. The CRC design seeks to optimize the frame error rate (FER) performance of the code resulting from the concatenation of the CRC and the CC. Utilization of the dual trellis proposed by Yamada \emph{et al.} lowers the complexity of CRC-aided serial list Viterbi decoding (SLVD) of ZTCCs and TBCCs. CRC-aided SLVD of the TBCCs closely approaches the RCU bound at a blocklength of $128$.

翻译：最近,以循环-冗余检查(CRC)辅助清单解码的零终止和尾尾咬混合代码(ZTCCs和TBCCs)的速率为1美元/美元/美元/美元/美元/美元/美元/美元/美元计算元计算元件计算元件,显示接近随机编码联盟(RCU)的短长的编码,本文件设计了以速率-美元(\omega-1)/美元/美元/千美元/美元计算元件短轮廓长度的CRC,同时考虑到ZT和TB案例。《儿童权利公约》的设计力求优化《儿童权利公约》和《CC》合并产生的代码的框架误差率(FER)。 利用Yamada\emphet{al.}提出的双轨,降低了《儿童权利公约》援助的ZTCCs和TBCCs Viterbi解码序列清单(SLVD)的复杂程度。《儿童权利公约》援助的TBCCs SLDs密切接近RCU的轮廓长度128美元。