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

If\ (Xᵢ, Yᵢ) \₈=₁^is a sequence of independent identically distributed discrete random pairs with (Xᵢ, Yᵢ) ~ p (x, y), Slepian and Wolf have shown that theXprocess and theYprocess can be separately described to a common receiver at ratesRXandRYhits per symbol ifRX + RY > H (X, Y), RX > H (X), RY > 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\ (Xᵢ, Yᵢ) \₈=₁^and countably infinite alphabets. The extension to an arbitrary number of processes is immediate.