Application of Gaussian approximation to iterative decoding with finite blocklengths

In this paper, the convergence analysis based on Gaussian approximation is extended to small and medium blocklengths. Gaussian approximation to extrinsic information has been instrumental in understanding and predicting the behavior of iterative decoding for codes that would allow iterative decoding such as turbo codes and LDPC codes. It enables a procedure to predict the "waterfall" region behavior where a steep slope of error rate curves is observed. As is well known, combination of transfer function and union bound techniques can be applied to predict the "error floor" region performance with necessary assumptions. This paper provides a framework to distinguish the different regions of behavior through defining a decoding failure probability.