  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.
