On the Entropy Region of Gaussian Random Variables

Understand

Given n (discrete or continuous) random variables X_i, the (2^n-1)-dimensional vector obtained by evaluating the joint entropy of all non-empty subsets of {X_1,...,X_n} is called an entropic vector.

• Determining the region of entropic vectors is an important open problem with many applications in information theory.
• Recently, it has been shown that the entropy regions for discrete and continuous random variables, though different, can be determined from one another.
• An important class of continuous random variables are those that are vector-valued and jointly Gaussian.