CRC-Aided List Decoding of Convolutional Codes in the Short Blocklength Regime
Hengjie Yang, Ethan M. Liang, Minghao Pan, Richard D. Wesel · IEEE Transactions on Information Theory · 2022
We consider the concatenation of a convolutional code (CC) with an optimized cyclic redundancy check (CRC) code as a promising paradigm for good short blocklength codes. The resulting CRC-aided convolutional code naturally permits the use of serial list Viterbi decoding (SLVD) to achieve maximum-likelihood decoding. The convolutional encoder of interest is of rate-$1/\omega $and the convolutional code is either zero-terminated (ZT) or tail-biting (TB). The resulting CRC-aided convolutional code is called a CRC-ZTCC or a CRC-TBCC. To design a good CRC-aided convolutional code, we propose thedistance-spectrum optimal (DSO)CRC polynomial. A DSO CRC search algorithm for the TBCC is provided. Our analysis reveals that the complexity of SLVD is governed by the expected list rank which converges to 1 at high SNR. This allows a good performance to be achieved with a small increase in complexity. In this paper, we focus on transmitting 64 information bits with a rate-1/2 convolutional encoder. For a target error probability$10^{-4}$, simulations show that the best CRC-ZTCC approaches the random-coding union (RCU) bound within 0.4 dB. Several CRC-TBCCs outperform the RCU bound at moderate SNR values.