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Recently, rate-1/n zero-terminated (ZT) and tail-biting (TB) convolutionalcodes (CCs) with cyclic redundancy check (CRC)-aided list decoding have beenshown to closely approach the random-coding union (RCU) bound for shortblocklengths. This paper designs CRC polynomials for rate- (n-1)/n ZT and TBCCs with short blocklengths. This paper considers both standard rate-(n-1)/n CCpolynomials and rate- (n-1)/n designs resulting from puncturing a rate-1/2code. The CRC polynomials are chosen to maximize the minimum distance d_min andminimize the number of nearest neighbors A_(d_min) . For the standardrate-(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 blocklengthof 128. This paper compares the FER performance (gap to the RCU bound) andcomplexity of the CRC-aided standard and punctured ZTCCs and TBCCs. This paperalso explores the complexity-performance trade-off for three TBCC decoders: asingle-trellis approach, a multi-trellis approach, and a modifiedsingle-trellis approach with pre-processing using the wrap around Viterbialgorithm.

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