External Codes for Multiple Unicast Networks via Interference Alignment

TL;DR

This paper models the multiple unicast network coding problem as an interference alignment issue over finite fields, establishing bounds on achievable rates and highlighting the impact of field characteristics.

Contribution

It introduces a formal interference alignment framework for finite field network coding and derives bounds with examples where these bounds are tight.

Findings

Outer bound for achievable rate region established

Examples demonstrating the bound's tightness

Field characteristic significantly influences network coding performance

Abstract

We introduce a formal framework to study the multiple unicast problem for a coded network in which the network code is linear over a finite field and fixed. We show that the problem corresponds to an interference alignment problem over a finite field. In this context, we establish an outer bound for the achievable rate region and provide examples of networks where the bound is sharp. We finally give evidence of the crucial role played by the field characteristic in the problem.