A Gilbert bound for periodic binary convolutional codes

A Gilbert bound for periodic binary convolutional (PBC) codes is established. This bound shows that regardless of previous decoding decisions any fraction of errors less thanalpha/2can be corrected in a constraint length by some PBC code if the constraint length is sufficiently large andR, the code rate, is less than1 - H(alpha)]/2, 0 leq alpha < frac{1}{2}.