  The optimal rate region for interference networks is characterized when
encoding is restricted to random code ensembles with superposition coding and
time sharing. A simple simultaneous nonunique decoding rule, under which each
receiver decodes for the intended message as well as the interfering messages,
is shown to achieve this optimal rate region regardless of the relative
strengths of signal, interference, and noise. This result implies that the
Han-Kobayashi bound, the best known inner bound on the capacity region of the
two-user-pair interference channel, cannot be improved merely by using the
optimal maximum likelihood decoder.
