EXIT Chart Approximations using the Role Model Approach

TL;DR

This paper introduces a new approximation called mixed information for estimating EXIT functions, enabling analysis of complex decoders with large message alphabets or non-distributional messages, using the role model approach.

Contribution

It proposes the mixed information approximation and demonstrates its application in optimizing non-binary LDPC decoders via the role model approach.

Findings

Mixed information provides a lower bound for true EXIT functions.

The role model approach can optimize decoder post-processing.

The method is effective even with unknown code-symbols.

Abstract

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.