When a scarce state transition (SST) Viterbi decoder is used to decode general nonsystematic convolutional codes (not included among quick look-in (QLI) codes), metrics based on the maximum a posteriori probability (MAP) estimation method must be computed in order for the main decoder to operate under the criterion of minimizing the decoding error probability. in this case, however, it becomes necessary to extend the original code trellis structure by introducing augmented trellis states in order to incorporate the newly induced correlation among the apparent information sequence.
This paper shows that the extended trellis degenerates into the original one as the channel error probability q approaches one-half. By performing an equivalent transformation of metrics, it is shown also that the branch metrics derived based on the MAP estimation method converge to those computed using the conventional one as q approaches one-half.