The rate region of secure symmetrical multilevel diversity coding

This paper considers the problem of secure symmetrical multilevel diversity coding. It is shown that a simple separate encoding scheme known as superposition coding can achieve the entire admissible rate region of the problem. Key to our proof is to establish a nontrivial conditional version of a subset entropy inequality of Yeung and Zhang, which was previously used to prove the optimality of superposition coding in terms of achieving the entire admissible rate region of the classical symmetrical multilevel diversity coding problem without any secrecy constraint.