ML performances of serial turbo codes do not concentrate!

In this paper we investigate the typical behaviour of minimum distance and ML word error probability of a serial turbo concatenation with random interleaver, when the interleaver length N goes to infinity. Our main result shows that the word error probability P(e) goes to zero subexponentially in N with probability one. While it is known that 10glE[P(e)]/logN converges to a constant, we prove that with probability one the sequence 10g(-log(P(e)))/logN approaches an interval [α, β] C (0 ,1 ), thus showing that the expected error rate is dominated by an asymptotically negligible fraction of bad interleavers. Our analysis is based on precise estimations of the minimum distance distribution