We show that the ensemble average of the block error probability for t
he ensemble of terminated rate 1/n fixed convolutional codes, used on
the binary symmetric channel with a maximum likelihood decoder, is bou
nded by exp(2) - NE(r)(1 - K/N), where N = (L + m)n is the block lengt
h, L being the message length, K the constraint length, and E(r)() is
the random coding exponent for block codes. Hence, E(r)(1 - K/N) > 0 f
or H(p) < K/N less than or equal to 1, where H() is the binary entropy
function and p is the cross-over probability of the binary symmetric
channel.