  We consider a scenario wherein two parties Alice and Bob are provided
$X_{1}^{n}$ and $X_{2}^{n}$ -- samples that are IID from a PMF $P_{X_1 X_2}$.
Alice and Bob can communicate to Charles over (noiseless) communication links
of rate $R_1$ and $R_2$ respectively. Their goal is to enable Charles generate
samples $Y^{n}$ such that the triple $(X_{1}^{n},X_{2}^{n},Y^{n})$ has a PMF
that is close, in total variation, to $\prod P_{X_1 X_2 Y}$. In addition, the
three parties may posses pairwise shared common randomness at rates $C_1$ and
$C_2$. We address the problem of characterizing the set of rate quadruples
$(R_1,R_2,C_1,C_2)$ for which the above goal can be accomplished. We provide a
set of sufficient conditions, i.e. an inner bound to the achievable rate
region, and necessary conditions, i.e. an outer bound to the rate region for
this three party setup. We provide a joint-typicality based random coding
argument involving encoding and decoding operations to perform soft covering
and a pertinent relaxation of the PMF requirement for the encoders.
