On the Distribution of Extrinsic L-values in Gray-mapped 16-QAM

In this paper we address the issue of probabilistic modelling of the extrinsic L-values, used as reliability metrics in the context of bit interleaved coded modulation with iterative demapping (BICM-ID). Starting with a simple piece-wise linear model of the L-values obtained via the max-log ap-proximation, we derive the expressions for the cumulative distribution functions of the L-values, that differentiated produce the desired forms of the probability density functions. To illustrate the usefulness of our analytical expressions we applied them to efficiently compute the so-called EXIT functions of the demapper for different values of SNR. The proposed analytical expressions are also compared to the histograms of the L-values obtained through much more time-consuming simulations