A class of non-Shannon-type information inequalities and their applications

Information inequalities form the most important set of tools for proving converse coding theorems in information theory problems. They are sometimes referred to as the “Laws of Information Theory,” because they govern the impossibilities in information theory. For a long time, all information inequalities we knew were nothing but simple consequences of the nonnegativity of Shannon´s information measures. Owing to the recent discovery of a few so-called non-Shannon-type information inequalities, it is now known that there are laws in information theory beyond those laid down by Shannon. In this paper, we show that the unconditional inequality discovered by the authors (1998) in fact implies a class of 2¹⁴ non-Shannon-type inequalities, and we show possible applications of these inequalities in information theory problems