  Intrapartum fetal heart rate (FHR) monitoring constitutes a reference tool in
clinical practice to assess the baby health status and to detect fetal
acidosis. It is usually analyzed by visual inspection grounded on FIGO
criteria. Characterization of Intrapartum fetal heart rate temporal dynamics
remains a challenging task and continuously receives academic research efforts.
Complexity measures, often implemented with tools referred to as
\emph{Approximate Entropy} (ApEn) or \emph{Sample Entropy} (SampEn), have
regularly been reported as significant features for intrapartum FHR analysis.
We explore how Information Theory, and especially {\em auto mutual information}
(AMI), is connected to ApEn and SampEn and can be used to probe FHR dynamics.
Applied to a large (1404 subjects) and documented database of FHR data,
collected in a French academic hospital, it is shown that i) auto mutual
information outperforms ApEn and SampEn for acidosis detection in the first
stage of labor and continues to yield the best performance in the second stage;
ii) Shannon entropy increases as labor progresses, and is always much larger in
the second stage;iii) babies suffering from fetal acidosis additionally show
more structured temporal dynamics than healthy ones and that this progressive
structuration can be used for early acidosis detection.
