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The authors consider a multi-way relay network with an orthogonal uplink and correlated sources, and they characterize reliable communication (in the usual Shannon sense) with a single-letter expression. The characterization is obtained using a joint source-channel random-coding argument, which is based on a combination of Wyner et al.'s Cascaded Slepian-Wolf Source Coding and Tuncel's Slepian-Wolf Coding over Broadcast Channels. They prove a separation theorem for the special case of two nodes; that is, they show that modular code architecture with separate source and channel coding functions is (asymptotically) optimal. Finally, they propose a practical coding scheme based on low-density parity-check codes, and they analyze its performance using multi-edge density evolution.
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