Computation over Multiple-Access Channels
IEEE Transactions on Information Theory, Special Issue on Models, Theory, and Codes for Relaying and Cooperation in Communication Networks, vol.53, no.10, pp.3498-3516, October 2007.
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The problem of reliably reconstructing a function of sources over a multiple-access channel is considered. It is shown that there is no source-channel separation theorem even when the individual sources are independent. Joint source-channel strategies are developed that are optimal when the structure of the channel probability transition matrix and the function are appropriately matched. Even when the channel and function are mismatched, these computation codes often outperform separation-based strategies. Achievable distortions are given for the distributed refinement of the sum of Gaussian sources over a Gaussian multiple-access channel with a joint source-channel lattice code. Finally, computation codes are used to determine the multicast capacity of finite field multiple-access networks, thus linking them to network coding.
B. Nazer and M. Gastpar, Computation over Multiple-Access Channels, IEEE Transactions on Information Theory, vol.53, no.10, pp.3498-3516, October 2007.