  The non-interactive source simulation (NISS) scenario is considered. In this
scenario, a pair of distributed agents, Alice and Bob, observe a distributed
binary memoryless source $(X^d,Y^d)$ generated based on joint distribution
$P_{X,Y}$. The agents wish to produce a pair of discrete random variables
$(U_d,V_d)$ with joint distribution $P_{U_d,V_d}$, such that $P_{U_d,V_d}$
converges in total variation distance to a target distribution $Q_{U,V}$ as the
input blocklength $d$ is taken to be asymptotically large. Inner and outer
bounds are obtained on the set of distributions $Q_{U,V}$ which can be produced
given an input distribution $P_{X,Y}$. To this end, a bijective mapping from
the set of distributions $Q_{U,V}$ to a union of star-convex sets is provided.
By leveraging proof techniques from discrete Fourier analysis along with a
novel randomized rounding technique, inner and outer bounds are derived for
each of these star-convex sets, and by inverting the aforementioned bijective
mapping, necessary and sufficient conditions on $Q_{U,V}$ and $P_{X,Y}$ are
provided under which $Q_{U,V}$ can be produced from $P_{X,Y}$. The bounds are
applicable in NISS scenarios where the output alphabets $\mathcal{U}$ and
$\mathcal{V}$ have arbitrary finite size. In case of binary output alphabets,
the outer-bound recovers the previously best-known outer-bound.
