  Alphabet size of auxiliary random variables in our canonical description is
derived. Our analysis improves upon estimates known in special cases, and
generalizes to an arbitrary multiterminal setup. The salient steps include
decomposition of constituent rate polytopes into orthants, translation of a
hyperplane till it becomes tangent to the achievable region at an extreme
point, and derivation of minimum auxiliary alphabet sizes based on
Caratheodory's theorem.
