  This paper extends the well-known source coding problem of multiple
descriptions, in its general and basic setting, to analog source-channel coding
scenarios. Encoding-decoding functions that optimally map between the (possibly
continuous valued) source and the channel spaces are numerically derived. The
main technical tool is a non-convex optimization method, namely, deterministic
annealing, which has recently been successfully used in other mapping
optimization problems. The obtained functions exhibit several interesting
structural properties, map multiple source intervals to the same interval in
the channel space, and consistently outperform the known competing mapping
techniques.
