Reciprocity in Linear Deterministic Networks under Linear Coding

TL;DR

This paper proves that in linear deterministic networks with multiple unicast flows, the rate regions are identical for a network and its reciprocal when using linear coding, extending known reversibility results.

Contribution

It demonstrates the linear reversibility of rate regions in multi-unicast linear deterministic networks, generalizing previous wireline network results.

Findings

Rate regions are identical for a network and its reciprocal.

Reversibility holds under linear coding in multi-unicast scenarios.

Extends linear reversibility to more general network models.

Abstract

The linear deterministic model has been used recently to get a first order understanding of many wireless communication network problems. In many of these cases, it has been pointed out that the capacity regions of the network and its reciprocal (where the communication links are reversed and the roles of the sources and the destinations are swapped) are the same. In this paper, we consider a linear deterministic communication network with multiple unicast information flows. For this model and under the restriction to the class of linear coding, we show that the rate regions for a network and its reciprocal are the same. This can be viewed as a generalization of the linear reversibility of wireline networks, already known in the network coding literature.