Symmetrical Multilevel Diversity Coding (SMDC) is a network compression problem,
for which separate coding was shown to be optimal in terms of achieving the
entire admissible rate region by Yeung and Zhang in 1999. Key to their proof is
a generalization of the classical subset entropy inequality of Han. This talk
presents a simplified proof of the generalized subset inequality of Han. The
proof is based on a subset entropy inequality recently established by Madiman
and Tetali and a linear-programing result that we lift from the original proof
of Yeung and Zhang. We show that this simplified proof allows a further
generalization of the generalized subset inequality of Han, which we use to
establish the optimality of separate encoding for the secure SMDC problem.