ML Performances of Serial Turbo Codes do not Concentrate!

Konferenz: TURBO - CODING - 2006 - 4th International Symposium on Turbo Codes & Related Topics; 6th International ITG-Conference on Source and Channel Coding
03.04.2006 - 07.04.2006 in Munich, Germany

Tagungsband: TURBO - CODING - 2006

Seiten: 6Sprache: EnglischTyp: PDF

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Como, Giacomo; Garin, Federica; Fagnani, Fabio (Dipartimento di Matematica, Politecnico di Torino, Duca degli Abruzzi 24, 10129 Torino, Italy)

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.