Upper bounds on the probability of the correct path loss for list decoding of fixed convolutional codes

In list decoding (M-algorithm) the decoder state space is typically much smaller than the encoder state space. Hence, it can happen that the correct path is lost. This is a serious kind of error event that is typical for list decoding. In this paper two upper bounds on the probability of correct path loss for list decoding are given. For fixed convolutional codes counterparts to Viterbi's upper bounds for maximum-likelihood decoding of fixed convolutional codes are proved. Finally, it is shown that there exists a fixed convolutional code whose probability of correct path loss when decoded by list decoding satisfies a simple expurgated bound.