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Function computation of arbitrarily correlated discrete sources over Gaussiannetworks with orthogonal components is studied. Two classes of functions areconsidered: the arithmetic sum function and the type function. The arithmeticsum function in this paper is defined as a set of multiple weighted arithmeticsums, which includes averaging of the sources and estimating each of thesources as special cases. The type or frequency histogram function counts thenumber of occurrences of each argument, which yields many important statisticssuch as mean, variance, maximum, minimum, median, and so on. The proposedcomputation coding first abstracts Gaussian networks into the correspondingmodulo sum multiple-access channels via nested lattice codes and linear networkcoding and then computes the desired function by using linear Slepian-Wolfsource coding. For orthogonal Gaussian networks (with no broadcast andmultiple-access components), the computation capacity is characterized for aclass of networks. For Gaussian networks with multiple-access components (butno broadcast), an approximate computation capacity is characterized for a classof networks.

Computation Over Gaussian Networks With Orthogonal Components