  The randomized fixe-composition with optimal decoding error exponents are
studied \cite{Raul_ISIT,Raul_journal} for the finite alphabet interference
channel (IFC) with two transmitter-receiver pairs. In this paper we investigate
the capacity region of the randomized fixed-composition coding scheme. A
complete characterization of the capacity region of the said coding scheme is
given. The inner bound is derived by showing the existence of a positive error
exponent within the capacity region. A simple universal decoding rule is given.
The tight outer bound is derived by extending a technique first developed in
\cite{Dueck_RC} for single input output channels to interference channels. It
is shown that even with a sophisticated time-sharing scheme among randomized
fixed-composition codes, the capacity region of the randomized
fixed-composition coding is not bigger than the known Han-Kobayashi
\cite{Han_Kobayashi} capacity region. This suggests that the average behavior
of random codes are not sufficient to get new capacity regions.
