  We present an interleaving scheme that yields quasi-cyclic turbo codes. We
prove that randomly chosen members of this family yield with probability almost
1 turbo codes with asymptotically optimum minimum distance, i.e. growing as a
logarithm of the interleaver size. These interleavers are also very practical
in terms of memory requirements and their decoding error probabilities for
small block lengths compare favorably with previous interleaving schemes.
