On the Non-robustness of Essentially Conditional Information Inequalities

Tarik Kaced (1) , Andrei Romashchenko (1)

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We show that two essentially conditional linear inequalities for Shannon's entropies (including the Zhang- Yeung'97 conditional inequality) do not hold for asymptotically entropic points. This means that these inequalities are non-robust in a very strong sense. This result raises the question of the meaning of these inequalities and the validity of their use in practice-oriented applications.

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Tarik Kaced, Andrei Romashchenko. On the Non-robustness of Essentially Conditional Information Inequalities. ITW'12: Information Theory Workshop, Sep 2012, Switzerland. pp.1935-1939. ⟨lirmm-00736192⟩