On the minimum distance of parallel and serially concatenated codes

We show that with high probability the minimum distance of parallel concatenated codes with k parallel branches and recursive component codes grows like n^k-2k/ in the interleaving length n. In particular, this growth rate is independent of the choice of recursive component codes. As a specific case, the minimum distance of standard turbo codes with only two branches does not grow like any power of n. For serially concatenated codes with two recursive component codes the minimum distance grows with high probability like n(d*₀-2/d*₀), where d₀* is the free distance of the outer code. The result is still valid if the outer encoder is non-recursive