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 than
\alpha/2
can be corrected in a constraint length by some PBC code if the constraint length is sufficiently large and
R
, the code rate, is less than
[1 - H(\alpha)]/2, 0 \leq \alpha < \frac{1}{2}
.