Proving and disproving information inequalities

Proving an information inequality is a crucial step in establishing the converse results in coding theorems. However, an information inequality involving many random variables is difficult to be proved manually. In [1], Yeung developed a framework that uses linear programming for verifying linear information inequalities. Under this framework, this paper considers a few other problems that can be solved by using Lagrange duality and convex approximation. We will demonstrate how linear programming can be used to find an analytic proof of an information inequality. The way to find a shortest proof is explored. When a given information inequality cannot be proved, the sufficient conditions for a counterexample to disprove the information inequality are found by linear programming.