#### Campus Units

Electrical and Computer Engineering

#### Document Type

Article

#### Publication Version

Submitted Manuscript

#### Publication Date

11-7-2016

#### Journal or Book Title

arXiv

#### Volume

Cs.IT

#### First Page

1611.01887

#### Abstract

A sum-network is an instance of a network coding problem over a directed acyclic network in which each terminal node wants to compute the sum over a finite field of the information observed at all the source nodes. Many characteristics of the well-studied multiple unicast network communication problem also hold for sum-networks due to a known reduction between instances of these two problems. In this work, we describe an algorithm to construct families of sum-network instances using incidence structures. The computation capacity of several of these sum-network families is characterized. We demonstrate that unlike the multiple unicast problem, the computation capacity of sum-networks depends on the characteristic of the finite field over which the sum is computed. This dependence is very strong; we show examples of sum-networks that have a rate-1 solution over one characteristic but a rate close to zero over a different characteristic. Additionally, a sum-network can have an arbitrary different number of computation capacities for different alphabets. This is contrast to the multiple unicast problem where it is known that the capacity is independent of the network coding alphabet.

#### Copyright Owner

The authors

#### Copyright Date

2017

#### Language

en

#### File Format

application/pdf

#### Recommended Citation

Tripathy, Ardhendu and Ramamoorthy, Aditya, "Sum-networks from incidence structures: construction and capacity analysis" (2016). *Electrical and Computer Engineering Publications*. 107.

https://lib.dr.iastate.edu/ece_pubs/107