Aspects of Information Inequalities and their Applications
Information inequalities are well-known as the basic laws governing the fundamental limits in data transmission and compression. They are critical tools in proving converse coding theorems in communications. These inequalities are also closely related to other areas including matroid theory, group theory, linear algebra, algorithmic complexity, determinantal inequalities and many others. In this talk, we will cover various interesting aspects of information inequalities and entropic polymatroids. Relations between inequalities for groups and information inequalities will be derived and properties for entropic polymatroids induced by groups and vector spaces will be discussed. As an application, we will also demonstrate how information inequalities can be used to characterise throughput in networks.