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 than

can be corrected in a constraint length by some PBC code if the constraint length is sufficiently large and

, the code rate, is less than
![[1 - H(\\alpha )]/2, 0 \\leq \\alpha < frac{1}{2}](/images/tex/7973.gif)
.