Unified-Theory-of-Source-Coding-Part-I-–-Two-Terminal-Problems.pdfVIP

Unified Theory of Source Coding: Part I – Two Terminal Problems Soumya Jana University of Illinois at Urbana-Champaign Email: jana@uiuc.edu Abstract Since the publication of Shannon’s theory of one terminal source coding, a num- ber of interesting extensions have been derived by researchers such as Slepian-Wolf, Wyner, Ahlswede-K¨orner, Wyner-Ziv and Berger-Yeung. Specifically, the achievable rate or rate-distortion region has been described by a first order information-theoretic functional of the source statistics in each of the above cases. At the same time sev- eral problems have also remained unsolved. Notable two terminal examples include the joint distortion problem, where both sources are reconstructed under a combined distortion criterion, as well as the partial side information problem, where one source is reconstructed under a distortion criterion using information about the other (side information) available at a certain rate (partially). In this paper we solve both of these open problems. Specifically, we give an infinite order description of the achievable rate- distortion region in each case. In our analysis we set the above problems in a general framework and formulate a unified methodology that solves not only the problems at hand but any two terminal problem with noncooperative encoding. The key to such unification is held by a fundamental source coding principle which we derive by ex- tending the typicality arguments of Shannon and Wyner-Ziv. Finally, we demonstrate the expansive scope of our technique by re-deriving known coding theorems. We shall observe that our infinite order descriptions simplify to the expected first order in the known special cas