Computing in Additive Networks with Bounded-Information Codes

TL;DR

This paper introduces a new random coding technique for additive wireless networks that ensures bounded information per neighborhood, enabling efficient solutions to fundamental distributed problems.

Contribution

It presents a novel coding method and algorithms that guarantee bounded information in each neighborhood, improving computation in additive network models.

Findings

Efficient algorithms for symmetry breaking and network parameter approximation.

A new random coding technique enabling successful decoding with limited information.

Improved understanding of information constraints in additive wireless networks.

Abstract

This paper studies the theory of the additive wireless network model, in which the received signal is abstracted as an addition of the transmitted signals. Our central observation is that the crucial challenge for computing in this model is not high contention, as assumed previously, but rather guaranteeing a bounded amount of \emph{information} in each neighborhood per round, a property that we show is achievable using a new random coding technique. Technically, we provide efficient algorithms for fundamental distributed tasks 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 to successfully decode the received information, as long as it does not contain too many distinct values. We then design our algorithms to produce a limited amount of information in each neighborhood in order to leverage our enriched toolbox for computing in additive networks.