Fundamental Limits on A Class of Secure Asymmetric Multilevel Diversity Coding Systems

In future communication applications, users may obtain their messages that have different importance levels distributively from several available sources, such as distributed storage or even devices belonging to other users. This scenario is best modeled by the multilevel diversity coding systems (MDCS). To achieve perfect (information-theoretic) secrecy against wiretap channels, this paper investigates the fundamental limits on the secure rate region of the asymmetric multilevel diversity coding systems (AMDCS), which include the symmetric case as a special case. Threshold perfect secrecy is added to the AMDCS model. The eavesdropper may have access to any one but not more than one subset of the channels but know nothing about the sources, as long as the size of the subset is not above the security level. The question of whether superposition (source separation) coding is optimal for such an AMDCS with threshold perfect secrecy is answered. A class of secure AMDCS (S-AMDCS) with an arbitrary number of encoders is solved and it is shown that linear codes are optimal for this class of instances. However, in contrast with the secure symmetric multilevel diversity coding systems (S-SMDCS), superposition is shown to be not optimal for S-AMDCS in general. In addition, necessary conditions on the existence of a secrecy key are determined as a design guideline.