Communicating the sum of sources over a network

TL;DR

This paper analyzes the capacity of network coding in directed acyclic graphs to enable terminals to recover the sum of sources, providing exact rate regions for specific source-terminal configurations.

Contribution

It characterizes the rate region for sum recovery in networks with two sources and multiple terminals, and with multiple sources and two terminals, under certain connectivity conditions.

Findings

Existence of coding vector assignments for sum recovery

Rate region characterized for specific source-terminal configurations

Sum can be recovered if each source connects to each terminal

Abstract

We consider a network (that is capable of network coding) with a set of sources and terminals, where each terminal is interested in recovering the sum of the sources. Considering directed acyclic graphs with unit capacity edges and independent, unit-entropy sources, we show the rate region when (a) there are two sources and $n$ terminals, and (b) $n$ sources and two terminals. In these cases as long as there exists at least one path from each source to each terminal we demonstrate that there exists a valid assignment of coding vectors to the edges such that the terminals can recover the sum of the sources.