High-Rate Convolutional Codes with CRC-Aided List Decoding for Short Blocklengths

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 $128$.Comment: 6 pages; submitted to 2022 IEEE International Conference on Communications (ICC 2022

CRC-Aided High-Rate Convolutional Codes With Short Blocklengths for List Decoding

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.Comment: arXiv admin note: substantial text overlap with arXiv:2111.0792