List-Decoded Tail-Biting Convolutional Codes with Distance-Spectrum Optimal CRCS for 5G

This paper uses convolutional codes (CCs) with distance-spectrum optimal (DSO) cyclic redundancy checks (CRCs) and the serial list Viterbi algorithm (S-LVA) to approach the random coding union (RCU) bound with low decoding complexity at the target FER. We show, for example, that a 64-state zero-terminated CC with a DSO CRC can achieve performance within 0.5 dB of the RCU bound for information blocklength k=64 at FER of 10^-3. We also show that a tail-biting CC with a DSO CRC can achieve even better performance, within 0.05 dB of the RCU bound at FER of 10^-4 for a 256-state CC with k=64. This paper provides analysis of decoding complexity, which for S-LVA depends on the expected list size. We show that if the target FER is low enough, the expected list size approaches one so that the average complexity of S-LVA approaches that of standard soft Viterbi on the CC, i.e., with no list decoding. We also provide DSO CRCs for CCs with k=64 and rates of 1/2, 1/3, 1/6 and 1/12 for the 5G new radio control channel and compare their performance with polar codes.