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

TL;DR

This paper presents a joint design methodology for convolutional and CRC codes optimized for serial list Viterbi decoding, balancing error performance and decoding complexity.

Contribution

It introduces a joint design criterion based on coded channel capacity and SNR gap, and analyzes the performance and optimal configurations of CC-CRC pairs under S-LVA.

Findings

Optimal list size equals the total number of CCs.

The best CC-CRC pair minimizes SNR gap with target FER.

Weaker convolutional codes can match stronger codes with optimal CRCs.

Abstract

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.