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

Recently, rate-<inline-formula> <tex-math notation="LaTeX">$1/n$ </tex-math></inline-formula> 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-<inline-formula> <tex-math notation="LaTeX">$(n-1)/n$ </tex-math></inline-formula> ZT and TB CCs with short blocklengths. This paper considers both standard rate-<inline-formula> <tex-math notation="LaTeX">$(n-1)/n$ </tex-math></inline-formula> CC polynomials and rate-<inline-formula> <tex-math notation="LaTeX">$(n-1)/n$ </tex-math></inline-formula> designs resulting from puncturing a rate-<inline-formula> <tex-math notation="LaTeX">$1/2$ </tex-math></inline-formula> code. The CRC polynomials are chosen to maximize the minimum distance <inline-formula> <tex-math notation="LaTeX">$d_{\min }$ </tex-math></inline-formula> and minimize the number of nearest neighbors <inline-formula> <tex-math notation="LaTeX">$A_{d_{\min }}$ </tex-math></inline-formula>. For the standard rate-<inline-formula> <tex-math notation="LaTeX">$(n-1)/n$ </tex-math></inline-formula> 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.