https://doi.org/10.1007/PL00011086
The statistical mechanics of turbo codes
1
Scuola Normale Superiore and INFN Sezione di Pisa,
56100 Pisa, Italy
2
Laboratoire de Physique Théorique de l'École Normale
SupérieureUMR 8549, Unité Mixte de Recherche du
Centre National de la Recherche Scientifique et de
l'École Normale Supérieure., 24 rue Lhomond, 75231 Paris Cedex 05, France
Received:
14
March
2000
Revised:
17
July
2000
Published online: 15 November 2000
The "turbo codes", recently proposed by Berrou
et al. [1]
are written as a disordered spin Hamiltonian. It is shown
that there exists a threshold Θ such that
for signal to noise ratios 
the error probability per
bit vanishes in the thermodynamic limit, i.e. the limit of infinitely
long sequences. The value of the threshold has been computed for
two particular turbo codes. It is found that it depends on the code. These
results are compared with numerical simulations.
PACS: 75.10.Hk – Classical spin models / 75.10.Nr – Spin-glass and other random models / 89.70.+c – Information science
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
