Bounds and approximations for the bit error probability of convolutional codes

The bit error probability P_b of convolutional codes decoded using the Viterbi algorithm using both soft and hard decision techniques is considered. Approximations to the additive or union upper bound on P_b which also form good approximations to P_b at values up to 10^-2 or higher are presented. Tables are given for the best codes listed for constraint lengths between 3 and 7 and rates 1/2 and 1/3.