In this paper 1 we consider the communication problem that involves transmission of correlated sources over broadcast channels. We consider a graph-based framework for this information transmission problem. The system involves a source coding module and a channel coding module. In the source coding module, the sources are efficiently represented using a nearly semi-regular bipartite graph, and the in the channel coding module, the edges of this graph are reliably transmitted over a broadcast

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... nnel. We consider nearly semi-regular bipartite graphs as discrete interface between source coding and channel coding in this multiterminal setting. In particular, in this paper, we restrict our attention to the source coding module, building on our earlier work on the channel coding module. We provide an information-theoretic characterization of the rate of growth of the exponent (as a function of the number source samples) of the size of such graphs that can reliably represent a pair of correlated sources.