ML Performances of Serial Turbo Codes do not Concentrate!

Inhalt:
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 log E[P(e)]/ logN converges to a constant, we prove that with probability one the sequence log(-log(P(e)))/ log N 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.