Conditional Information Inequalities for Entropic and Almost Entropic Points

Tarik Kaced (1) , Andrei Romashchenko (2)

1 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 ESCAPE - Systèmes complexes, automates et pavages

We study conditional linear information inequalities, i.e., linear inequalities for Shannon entropy that hold for distributions whose entropies meet some linear constraints. We prove that some conditional information inequalities cannot be extended to any unconditional linear inequalities. Some of these conditional inequalities hold for almost entropic points, while others do not. We also discuss some counterparts of conditional information inequalities for Kolmogorov complexity.

Mots clés: Information inequalities; non-Shannon-type inequalities; conditional inequalities; almost entropic points; Kolmogorov complexity

Domaines: Mathématique discrète [cs.DM]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Probabilités [math.PR]

Tarik Kaced, Andrei Romashchenko. Conditional Information Inequalities for Entropic and Almost Entropic Points. IEEE Transactions on Information Theory, 2013, 59 (11), pp.7149-7167. ⟨10.1109/TIT.2013.2274614⟩. ⟨lirmm-00848455⟩