  A new inner bound on the capacity region of a general index coding problem is
established. Unlike most existing bounds that are based on graph theoretic or
algebraic tools, the bound is built on a random coding scheme and optimal
decoding, and has a simple polymatroidal single-letter expression. The utility
of the inner bound is demonstrated by examples that include the capacity region
for all index coding problems with up to five messages (there are 9846
nonisomorphic ones).
