EXIT chart approximations using the role model approach

Extrinsic Information Transfer (EXIT) functions can be measured by statistical methods if the message alphabet size is moderate or if messages are true a-posteriori distributions. We propose an approximation we call mixed information that constitutes a lower bound for the true EXIT function and can be estimated by statistical methods even when the message alphabet is large and histogram-based approaches are impractical, or when messages are not true probability distributions and time-averaging approaches are not applicable. We illustrate this with the hypothetical example of a rank-only message passing decoder for which it is difficult to compute or measure EXIT functions in the conventional way. We show that the role model approach [9] can be used to optimize post-processing for the decoder and that it coincides with Monte Carlo integration in the non-parametric case. It is guaranteed to tend towards the optimal Bayesian post-processing estimator and can be applied in a blind setup with unknown code-symbols to optimize the check-node operation for non-binary Low-Density Parity-Check (LDPC) decoders.