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

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.

Joint Design of Convolutional Code and CRC under Serial List Viterbi Decoding

This paper studies the joint design of optimal convolutional codes (CCs) and CRC codes when serial list Viterbi algorithm (S-LVA) is employed in order to achieve the target frame error rate (FER). We first analyze the S-LVA performance with respect to SNR and list size, repsectively, and prove the convergence of the expected number of decoding attempts when SNR goes to the extreme. We then propose the coded channel capacity as the criterion to jointly design optimal CC-CRC pair and optimal list size and show that the optimal list size of S-LVA is always the cardinality of all possible CCs. With the maximum list size, we choose the design metric of optimal CC-CRC pair as the SNR gap to random coding union (RCU) bound and the optimal CC-CRC pair is the one that achieves a target SNR gap with the least complexity. Finally, we show that a weaker CC with a strong optimal CRC code could be as powerful as a strong CC with no CRC code.