On the probability of error of convolutional codes

New upper and lower bounds and approximations on the sequence, event, first event, and bit-error probabilities of convolutional codes are presented. Each of these probabilities are precisely defined and the relationship between them described. Some of the new bounds and approximations are found to be very close to computer simulations at very high error ratios. Simple modifications to the traditional union upper bound are also described for both hard- and soft-decision channels that allow better performance estimates to be made.