Function Computation over Linear Channels

We consider multiple non-colocated sources communicating over a network to a common sink. We assume that the network operation is fixed, and its end result is to convey a fixed linear deterministic transformation of the source data to the sink. This linear transformation is known both at the sources and at the sink. We are interested in the problem of function computation over such networks. We design communication protocols that can perform computation without modifying the network operation, by appropriately selecting the codebook that the sources employ to map their measurements to the data they send over the network.