Identification of new classes of non-Shannon type constrained information inequalities and their relation to finite groups

The existence of the so called non-Shannon type (NST) information inequalities stems from the fact that the basic inequalities which are based on the non-negativity of Shannon´s information measures provide an incomplete characterization of the joint entropy function of n ≥ 4 discrete random variables (DRVs). Based on a certain NST inequality which was derived by Zhang and Yeung (1998), we identify new classes of NST constrained information inequalities which grow double exponentially with n (n ≥ 4), and generalize a previously reported result for n = 4. Relying on a fundamental relation between information theory and group theory which was devised by Chan and Yeung (see Proceedings 2000 IEEE International Symposium on Information Theory, p.492, Sorrento, Italy, June, 2000), we relate our discussion to finite groups.