Duality and the Value of Cooperation in Distributive Source and Channel Coding Problems ∗

This paper investigates the condition for duality between the achievable rate regions of the indirect distributive source coding problem and the broadcast channel. It has been shown previously that crucial to the existence of duality are two simultaneous Markov conditions that the joint distribution must satisfy. In this paper, we illustrate that the Markov conditions are satisfied if and only if distributive coding achieves the same sum rate as centralized coding under the same joint distribution. Thus, duality is closely related to the value of cooperation. Duality exists if and only if cooperation does not help. Several classes of channels in which duality exists are illustrated as examples. They include a generalization of a previous result on Gaussian multi-terminal source coding and a novel discrete memoryless broadcast channel for which Marton’s achievable rate region is optimal at the sum rate point.