  This paper identifies convolutional codes (CCs) used in conjunction with a
CC-specific cyclic redundancy check (CRC) code as a promising paradigm for
short blocklength codes. The resulting CRC-CC concatenated code naturally
permits the use of the serial list Viterbi decoding (SLVD) to achieve
maximum-likelihood decoding. The CC of interest is of rate-$1/\omega$ and is
either zero-terminated (ZT) or tail-biting (TB). For CRC-CC concatenated code
designs, we show how to find the optimal CRC polynomial for a given ZTCC or
TBCC. Our complexity analysis reveals that SLVD decoding complexity is a
function of the terminating list rank, which converges to one at high SNR. This
behavior allows the performance gains of SLVD to be achieved with a small
increase in average complexity at the SNR operating point of interest. With a
sufficiently large CC constraint length, the performance of CRC-CC concatenated
code under SLVD approaches the random-coding union (RCU) bound as the CRC size
is increased while average decoding complexity does not increase significantly.
TB encoding further reduces the backoff from the RCU bound by avoiding the
termination overhead. As a result, several CRC-TBCC codes outperform the RCU
bound at moderate SNR values while permitting decoding with relatively low
complexity.
