Deterministic Relay Networks with State Information

TL;DR

This paper characterizes the capacity of deterministic relay networks with state information, showing optimal rates when relay nodes process signals linearly, generalizing previous models and providing a unified framework for such networks.

Contribution

It introduces a unified approach to determine achievable and optimal rates in deterministic relay networks with state information, extending prior work on linear and erasure networks.

Findings

Achievable rate characterized for networks with full state knowledge at destinations.

Optimal rate achieved when relay nodes process signals linearly, meeting the cut-set bound.

Generalizes previous models to a unified framework for deterministic networks with state.

Abstract

Motivated by fading channels and erasure channels, the problem of reliable communication over deterministic relay networks is studied, in which relay nodes receive a function of the incoming signals and a random network state. An achievable rate is characterized for the case in which destination nodes have full knowledge of the state information. If the relay nodes receive a linear function of the incoming signals and the state in a finite field, then the achievable rate is shown to be optimal, meeting the cut-set upper bound on the capacity. This result generalizes on a unified framework the work of Avestimehr, Diggavi, and Tse on the deterministic networks with state dependency, the work of Dana, Gowaikar, Palanki, Hassibi, and Effros on linear erasure networks with interference, and the work of Smith and Vishwanath on linear erasure networks with broadcast.