Some bounds on the capacity of communicating the sum of sources

TL;DR

This paper investigates the capacity limits of directed acyclic networks where multiple sources generate independent processes over an abelian group, and all terminals aim to recover their sum, providing bounds based on network min-cut and source/terminal counts.

Contribution

It introduces bounds on the capacity of sum-networks considering network structure, min-cut, and source/terminal numbers, advancing understanding of network coding for sum recovery.

Findings

Derived bounds on sum-network capacity based on min-cut.

Established relationships between network parameters and capacity limits.

Provided theoretical insights into the solvability and capacity constraints of sum-networks.

Abstract

We consider directed acyclic networks with multiple sources and multiple terminals where each source generates one i.i.d. random process over an abelian group and all the terminals want to recover the sum of these random processes. The different source processes are assumed to be independent. The solvability of such networks has been considered in some previous works. In this paper we investigate on the capacity of such networks, referred as {\it sum-networks}, and present some bounds in terms of min-cut, and the numbers of sources and terminals.