Recently, rate-1/n zero-terminated (ZT) and tail-biting (TB) convolutional codes (CCs) 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 CRC polynomials for rate- (n-1)/n ZT and TB CCs with short blocklengths. This paper considers both standard rate-(n-1)/n CC polynomials and rate- (n-1)/n designs resulting from puncturing a rate-1/2 code. The CRC polynomials are chosen to maximize the minimum distance d_min and minimize the number of nearest neighbors A_(d_min) . For the standard rate-(n-1)/n codes, utilization of the dual trellis proposed by Yamada et al. lowers the complexity of CRC-aided serial list Viterbi decoding (SLVD). CRC-aided SLVD of the TBCCs closely approaches the RCU bound at a blocklength of 128. This paper compares the FER performance (gap to the RCU bound) and complexity of the CRC-aided standard and punctured ZTCCs and TBCCs. This paper also explores the complexity-performance trade-off for three TBCC decoders: a single-trellis approach, a multi-trellis approach, and a modified single-trellis approach with pre-processing using the wrap around Viterbi algorithm.

翻译：近期研究表明，采用循环冗余校验（CRC）辅助列表译码的码率1/n归零（ZT）与咬尾（TB）卷积码（CC）在短分组长度下能够紧密逼近随机编码联合（RCU）界。本文针对短分组长度下码率(n-1)/n的ZT与TB卷积码设计CRC多项式，同时考虑标准码率(n-1)/n卷积码多项式与通过删余1/2码率母码获得的(n-1)/n码率设计。CRC多项式的选取以最大化最小距离d_min并最小化最近邻居数A_(d_min)为目标。针对标准码率(n-1)/n码，采用Yamada等人提出的对偶网格可降低CRC辅助串行列表维特比译码（SLVD）复杂度。当分组长度为128时，CRC辅助TBCC的SLVD可紧密逼近RCU界。本文对比了采用CRC辅助标准与删余ZTCC及TBCC的误帧率性能（与RCU界的差距）及复杂度，并探索了三种TBCC译码器（单网格法、多网格法与基于环绕维特比算法预处理的改进单网格法）的复杂度-性能权衡。