A proof of the data compression theorem of Slepian and Wolf for ergodic sources (Corresp.)

If\{(X_i, Y_i)\}ᵢ₌₁∞is a sequence of independent identically distributed discrete random pairs with(X_i, Y_i) ~ p(x,y), Slepian and Wolf have shown that theXprocess and theYprocess can be separately described to a common receiver at ratesR_XandR_Yhits per symbol ifR_X + R_Y > H(X,Y), R_X > H(X), R_Y > H(Y). A simpler proof of this result will be given. As a consequence it is established that the Slepian-Wolf theorem is true without change for arbitrary ergodic processes\{(X_i,Y_i)\}ᵢ₌₁∞and countably infinite alphabets. The extension to an arbitrary number of processes is immediate.