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

  • Authors:

  • T. Cover

  • Affiliations:

  • -

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

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 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(XmidY), R_Y > H(YmidX). 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.