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This paper studies the theory of the additive wireless network model, inwhich the received signal is abstracted as an addition of the transmittedsignals. Our central observation is that the crucial challenge for computing inthis model is not high contention, as assumed previously, but ratherguaranteeing a bounded amount of \emph{information} in each neighborhood perround, a property that we show is achievable using a new random codingtechnique.  Technically, we provide efficient algorithms for fundamental distributedtasks in additive networks, such as solving various symmetry breaking problems,approximating network parameters, and solving an \emph{asymmetry revealing}problem such as computing a maximal input.  The key method used is a novel random coding technique that allows a node tosuccessfully decode the received information, as long as it does not containtoo many distinct values. We then design our algorithms to produce a limitedamount of information in each neighborhood in order to leverage our enrichedtoolbox for computing in additive networks.

Computing in Additive Networks with Bounded-Information Codes