Computation over Gaussian networks with orthogonal components

Function computation of arbitrarily correlated discrete sources over Gaussian networks with multiple access components but no broadcast is studied. Two classes of functions are considered: the arithmetic sum function and the frequency histogram function. The arithmetic sum function in this paper is defined as a set of multiple weighted arithmetic sums, which includes averaging of sources and estimating each of the sources as special cases. The frequency histogram function counts the number of occurrences of each argument, which yields many important statistics such as mean, variance, maximum, minimum, median, and so on. For a class of networks, an approximate computation capacity is characterized. The proposed approach first abstracts Gaussian networks into the corresponding modulo-sum multiple-access channels via lattice codes and linear network coding and then computes the desired function by using linear Slepian-Wolf source coding.