  We consider the asymmetric multilevel diversity (A-MLD) coding problem, where
a set of $2^K-1$ information sources, ordered in a decreasing level of
importance, is encoded into $K$ messages (or descriptions). There are $2^K-1$
decoders, each of which has access to a non-empty subset of the encoded
messages. Each decoder is required to reproduce the information sources up to a
certain importance level depending on the combination of descriptions available
to it. We obtain a single letter characterization of the achievable rate region
for the 3-description problem. In contrast to symmetric multilevel diversity
coding, source-separation coding is not sufficient in the asymmetric case, and
ideas akin to network coding need to be used strategically. Based on the
intuitions gained in treating the A-MLD problem, we derive inner and outer
bounds for the rate region of the asymmetric Gaussian multiple description (MD)
problem with three descriptions. Both the inner and outer bounds have a similar
geometric structure to the rate region template of the A-MLD coding problem,
and moreover, we show that the gap between them is small, which results in an
approximate characterization of the asymmetric Gaussian three description rate
region.
