A graph-based framework for transmission of correlated sources over multiuser channels

We consider a graph-based framework for transmission of correlated sources over multiuser channels. We show that a graph can be used as a discrete interface between the source coding and the channel coding for this multiterminal information transmission problem. We adopt a separation-based modular approach to this problem, involving a source coding module and a channel coding module. In the former module, the correlated sources are efficiently represented into correlated indices which can be associated with a graph. Then, in the latter module, these correlated indices, which correspond to the edges of this graph, can be reliably transmitted over the multiuser channel if the graph satisfies certain conditions. Here, the indices are encoded by using channel codewords which exploit the correlation structure of the messages. This leads to performance gains in terms of enlarging the class of correlated sources that, can be reliably transmitted over multiuser channels.; We apply our graph-based approach to many-to-one (called the multiple access channel) and one-to-many (called the broadcast channel) communication scenarios which are multiuser communication problems with a variety of applications. In the multiple access channel, many transmitters want to send their sources which are correlated to a single joint receiver reliably over the given channel. In the broadcast channel, a single transmitter wishes to send correlated sources reliably to many receivers over the channel.; As our main results for the multiple access channel, we provide achievable rate regions, which are information-theoretic characterizations of (1) the rate of exponential growth (as a function of the number of channel uses) of the size and the degrees of the bipartite graphs whose edges can be reliably transmitted over a multiple access channel, and (2) the rate of exponential growth (as a function of the number of source samples) of the size and the degrees of the bipartite graphs which can reliably represent a pair of correlated sources. Note that these two results can be combined only if two graphs satisfy certain conditions.; We also give similar results for the broadcast channel.