Stochastic models for turbo decoding

This paper proposes a stochastic framework for modelling and analysis of turbo decoding. By modelling the input and output signals of a turbo decoder as random processes, we prove that these signals become ergodic when the code block size becomes very large. This basic result allows us to easily model and compute the statistics of the signals in a turbo decoder. Using the ergodicity result and the fact that a sum of lognormal distributions is well approximated using a lognormal distribution, we show that the input-output signals in a turbo decoder, when expressed using the so-called scaled log-likelihood ratios, are well approximated using Gaussian distributions. Combining the two results above, we can model a turbo decoder using two inputs and two outputs (corresponding to the means and variances). Using this model, we have discovered that a typical decoding process is much more intricate than previously known, involving two regions of attractions, several fixed points, and a stable equilibrium manifold at which all decoding trajectories converge.