Serial List Viterbi Decoding with CRC: Managing Errors, Erasures, and Complexity

This paper analyzes the serial list Viterbi algorithm (S-LVA) used in conjunction with optimal CRC codes that minimize probability of undetected error by maximizing the minimum distance between convolutional codewords that pass the CRC check, following Lou et al. In particular, the paper identifies such optimal CRC codes for the 3GPP standard convolutional code (561,753). As SNR varies and the maximum list size L ranges from one to its maximum, this paper uses bounds, approximations, and simulation to characterize decoding complexity and the trade-off between erasure probability and undetected error probability. The complexity of S-LVA is captured by the expected value of the number of decoding attempts required before a CRC check passes or L codewords have been examined. For S-LVA with a degree-m CRC and maximum possible L, which is the cardinality of the set of all possible convolutional codewords, the expected value of the number of decoding attempts converges to one as SNR increases and to 2
^m
(1 - ϵ), for a small ϵ > 0, as SNR decreases. For S-LVA with the maximum possible L, the erasure probability is zero. As L decreases from this maximum, the erasure probability increases and the TIE probability decreases to that of L = 1, for which TIE probability is well approximated by a nearest-neighbor bound.