Duality of a Source Coding Problem and the Semi-Deterministic Broadcast Channel with Rate-Limited Cooperation

Ziv Goldfeld, Haim H. Permuter, Gerhard Kramer

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The Wyner-Ahlswede-Korner (WAK) empirical-coordination problem where the encoders cooperate via a finite-capacity one-sided link is considered. The coordination-capacity region is derived by combining several source coding techniques, such as Wyner-Ziv coding, binning, and superposition coding. Furthermore, a semi-deterministic (SD) broadcast channel (BC) with one-sided decoder cooperation is considered. Duality principles relating the two problems are presented, and the capacity region for the SD-BC setting is derived. The direct part follows from an achievable region for a general BC that is tight for the SD scenario. A converse is established by using telescoping identities. The SD-BC is shown to be operationally equivalent to a class of relay-BCs, and the correspondence between their capacity regions is established. The capacity region of the SD-BC is transformed into an equivalent region that is shown to be dual to the admissible region of the WAK problem in the sense that the information measures defining the corner points of both regions coincide. Achievability and converse proofs for the equivalent region are provided. For the converse, we use a probabilistic construction of auxiliary random variables that depends on the distribution induced by the codebook. Several examples illustrate the results.

Original languageEnglish
Article number7416198
Pages (from-to)2285-2307
Number of pages23
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - 1 May 2016


  • Channel and source duality
  • Semi-deterministic broadcast channel
  • cooperation
  • empirical coordination
  • multiterminal source coding
  • relay-broadcast channel

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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