Analyzing the turbo decoder using the Gaussian approximation

In this paper, we introduce a simple technique for analyzing the iterative decoder that is broadly applicable to different classes of codes defined over graphs in certain fading as well as AWGN channels, The technique is based on the observation that the extrinsic information from constituent MAP decoders is well approximated by Gaussian random variables when the inputs to the decoders are Gaussian. The independent Gaussian model implies the existence of an iterative decoder threshold that statistically characterizes the convergence of the iterative decoder. Despite the idealization of the model and the simplicity of the analysis technique, the predicted threshold values are in excellent agreement with the waterfall regions observed experimentally in the literature when the code word lengths are large.