Multiple access channels with arbitrarily correlated sources

Let \ (U₈, V₈) \₈=₁^n be a source of independent identically distributed (i. i. d. ) discrete random variables with joint probability mass function p (u, v) and common part w=f (u) =g (v) in the sense of Witsenhausen, Gacs, and Körner. It is shown that such a source can be sent with arbitrarily small probability of error over a multiple access channel (MAC) \ X₁ X₂, Y, p (y|x₁, x₂) \, with allowed codes \x₋ (u), x₂ (v) \ if there exist probability mass functions p (s), p (x₁|s, u), p (x₂|s, v), such that H (U|V) H (V|U) H (U, V|W) H (U, V) where p (s, u, v, x₁, x₂, y), Xl, X2, y) =p (s) p (u, v) p (x₁|u, s) p (x₂|v, s) p (y|x₁, x₂). lifts region includes the multiple access channel region and the Slepian-Wolf data compression region as special cases.