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

If
\{(X_i, Y_i)\}_{i=1}^{\infty}
is a sequence of independent identically distributed discrete random pairs with
(X_i, Y_i) ~ p(x,y)
, Slepian and Wolf have shown that the
X
process and the
Y
process can be separately described to a common receiver at rates
R_X
and
R_Y
hits per symbol if
R_X + R_Y > H(X,Y), R_X > H(X\midY), R_Y > H(Y\midX)
. 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}^{\infty}
and countably infinite alphabets. The extension to an arbitrary number of processes is immediate.