  We construct a Langlands parameterization of supercuspidal representations of
$G_2$ over a $p$-adic field. More precisely, for any finite extension $K /
\QQ_p$ we will construct a bijection \[ \CL_g : \CA^0_g(G_2,K) \rightarrow
\CG^0(G_2,K) \] from the set of generic supercuspidal representations of
$G_2(K)$ to the set of irreducible continuous homomorphisms $\rho : W_K \to
G_2(\CC)$ with $W_K$ the Weil group of $K$. The construction of the map is
simply a matter of assembling arguments that are already in the literature,
together with a previously unpublished theorem of G. Savin on exceptional theta
correspondences, included as an appendix. The proof that the map is a bijection
is arithmetic in nature, and specifically uses automorphy lifting theorems.
These can be applied thanks to a recent result of Hundley and Liu on
automorphic descent from $GL(7)$ to $G_2$.
