Fundamental Limits on a Class of Secure

Abstract—In the 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 the 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
MDCS (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 MDCS, 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.

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