# Communication and computation over erroneous networks

**Project Leader: **Girish Nair**Primary Contact: **Girish Nair (gnair@unimelb.edu.au)**Keywords: **distributed computing; distributed source coding; error control coding; network science; telecommunications**Disciplines: **Electrical & Electronic Engineering**Domains: **Networks and data in society, Optimisation of resources and infrastructure

Communication over networks of unidirectional channels is a well-studied problem in information theory, and is known to be difficult. The (ordinary) capacity regions for networks with multiple information sources are not generally known, and capacity-achieving codes are not guaranteed to be linear. In most of the literature on this topic, the objective is to reconstruct source signals with negligible error probability, or with bounds on expected distortion. Shannon's Information Theory is the main tool for finding capacity regions.

In this project, such networks will be studied when the objective is to obtain exactly zero errors, or when the distortion at each sink (i.e. destination) must satisfy worst-case bounds. The techniques will be based on nonstochastic information theory. [see Nair, IEEE Trans, Automatic Control, 2013; Nair, IEEE Conf. Decision and Control (CDC), Osaka, 2015]

An alternative goal may be for the sinks to evaluate a specified function of the source signals, such as their sum or median, to some specified tolerance. It is anticipated that if the network is a directed acyclic graph then structural routability conditions similar to [Nair, 2014] may be useful. However, if there are feedback links between network nodes, then a different angle is needed, based on “directed nonstochastic information”. [Nair, IEEE CDC 2012; Nair, IEEE CDC 2015]