  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 (arXiv:0809.1300) 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.
