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

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