Turbo codes: the phase transition

Turbo codes are a very efficient method for communicating reliably through a noisy channel. There is no theoretical understanding of their effectiveness. In reference [1] they are mapped onto a class of disordered spin models. The analytical calculations concerning these models are reported here. We prove the existence of a no-error phase and compute its local stability threshold. As a byproduct, we gain some insight into the dynamics of the decoding algorithm. Received 14 March 2000