Upper bound on the frame error probability of terminated trellis codes

The frame-error rate (FER) of trellis codes with trellis termination can be approximated by considering the length of the error events negligible with respect to the frame length. In this letter we prove that this approximation is actually a true upper bound. This may be useful to orientate the design of frame based transmission systems directly in terms of FER instead of the more common but less significant bit-error rate figure.