Symmetrical Multilevel Diversity Coding (SMDC) is a network compression problem for which a simple separate coding strategy known as superposition coding is optimal in terms of achieving the entire admissible rate region. Carefully constructed induction argument along with the classical subset entropy inequality of Han played a key role in proving the optimality. This thesis considers a generalization of SMDC for which, in addition to the randomly accessible encoders, there is also an all-access encoder. It is shown that superposition coding remains optimal in terms of achieving the entire admissible rate region of the problem. Key to our proof is to identify the supporting hyperplanes that define the boundary of the admissible rate region and then build on a generalization of Han's subset inequality. As a special case, the (R0,Rs) admissible rate region, which captures all possible tradeoffs between the encoding rate, R0, of the all-access encoder and the sum encoding rate, Rs, of the randomly accessible encoders, is explicitly characterized. To provide explicit proof of the optimality of superposition coding in this case, a new sliding-window subset entropy inequality is introduced and is shown to directly imply the classical subset entropy inequality of Han.