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Reliable Computation over Multiple-Access Channels

In the standard multiple-access problem, a central access point needs to reconstruct the signals observed by each user separately. Suppose now that the access point only reconstructs the sum (or any other function) of these observed signals. For this problem, we develop strategies and information-theoretic performance bounds. It is shown that in general, separating source from channel coding leads to suboptimal performance. For linear functions, a scheme is developed, analyzed, and shown to perform optimally for a class of multiple-access channels.