A Projection Method for Derivation of Non-Shannon-Type Information   Inequalities
  In 1998, Zhang and Yeung found the first unconditional non-Shannon-type information inequality. Recently, Dougherty, Freiling and Zeger gave six new unconditional non-Shannon-type information inequalities. This work generalizes their work and provides a method to systematically derive non-Shannon-type information inequalities. An application of this method reveals new 4-variable non-Shannon-type information inequalities. 
Weidong Xu, Jia Wang, Jun Sun