Non-Gaussian Behaviour of Extrinsic Log-Values

non-Gaussian behaviour of extrinsic Log-values (L-values) during iterative turbo-decoding process is investigated. I. Summary Extrinsic L-values are exchanged between the constituent log-APP decoders during each iteration of the turbo decoding process. It is this transfer of information that is critical in understanding the convergence behavior. In particular, Gaussian models have been used extensively. However, statistical tests on experimental data suggest that the Gaussian assumption is invalid. Fig. 1 plots the average extrinsic L-values skewness squared (β1) versus kurtosis (β2) at each decoder iteration while decoding a Berrou-Glavieux-Thitimajshima (BGT) Parallel Concatenated Convolutional Code (PCCC) [1]. Under the Gaussian assumption (β1, β2) would be a single fixed point at (0, 3) on Fig. 1. However, the measured (β1, β2) of the extrinsic L-values at each decoder iteration never exactly corresponds to Gaussian (unless by chance) but rather evolves along various points. A system of distributions that better reflects the (β1, β2) evolution is the Pearson family of density functions [2]. These distributions are solutions to the differential equation d ln f(x) d