On a new non-Shannon-type information inequality

Makarychev, Makarychev, Romashchenko and Vereshchagin (2001) discovered a new non-Shannon-type information inequality involving 5 random variables which can be viewed as a generalization of the ZY98 inequality of Zhang and Yeung (1998). We give a simple proof of this new inequality and explain its information theoretical meaning by formulating two information theoretical problems.