CRC-Aided List Decoding of Convolutional Codes in the Short Blocklength Regime

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