The turbo decoding algorithm and its phase trajectories

We analyze phase trajectories of the turbo decoding algorithm as a function of the signal-to-noise ratio (SNR). We prove the existence of fixed points not only at asymptotically high SNRs but also at asymptotically low SNRs. Fixed points at practical SNRs are empirically divided into two classes: indecisive fixed points which usually lead to numerous erroneous decisions and unequivocal fixed points which usually correspond to correct decisions. The waterfall region in the performance curve of turbo decoding is characterized as the region of transition from convergence to indecisive fixed points to convergence to unequivocal fixed points.