Linear Finite-Field Deterministic Networks With Many Sources and One Destination

TL;DR

This paper determines the capacity region of linear finite-field deterministic networks with multiple sources and one destination, accounting for interference and broadcast constraints, and provides conditions for source transmissibility.

Contribution

It establishes that the capacity region matches the cut-set bound and offers necessary and sufficient conditions for correlated source transmissibility.

Findings

Capacity region equals the cut-set region.

Conditions for transmissibility of correlated sources.

Relevance to wireless sensor networks.

Abstract

We find the capacity region of linear finite-field deterministic networks with many sources and one destination. Nodes in the network are subject to interference and broadcast constraints, specified by the linear finite-field deterministic model. Each node can inject its own information as well as relay other nodes' information. We show that the capacity region coincides with the cut-set region. Also, for a specific case of correlated sources we provide necessary and sufficient conditions for the sources transmissibility. Given the "deterministic model" approximation for the corresponding Gaussian network model, our results may be relevant to wireless sensor networks where the sensing nodes multiplex the relayed data from the other nodes with their own data, and where the goal is to decode all data at a single "collector" node.