Wireless Network Information Flow: A Deterministic Approach

TL;DR

This paper introduces a deterministic model for wireless networks to analyze maximum information flow and develops a practical scheme that nearly achieves this capacity in Gaussian networks, regardless of channel specifics.

Contribution

It provides an exact capacity characterization for deterministic wireless networks and proposes a universal quantize-map-and-forward scheme for Gaussian networks that approaches the cut-set bound.

Findings

Capacity of deterministic networks is characterized exactly.

The proposed scheme achieves within 1 bit/sec/Hz of the cut-set bound.

The scheme is universal and applicable to various network types.

Abstract

In a wireless network with a single source and a single destination and an arbitrary number of relay nodes, what is the maximum rate of information flow achievable? We make progress on this long standing problem through a two-step approach. First we propose a deterministic channel model which captures the key wireless properties of signal strength, broadcast and superposition. We obtain an exact characterization of the capacity of a network with nodes connected by such deterministic channels. This result is a natural generalization of the celebrated max-flow min-cut theorem for wired networks. Second, we use the insights obtained from the deterministic analysis to design a new quantize-map-and-forward scheme for Gaussian networks. In this scheme, each relay quantizes the received signal at the noise level and maps it to a random Gaussian codeword for forwarding, and the final destination decodes the source's message based on the received signal. We show that, in contrast to existing schemes, this scheme can achieve the cut-set upper bound to within a gap which is independent of the channel parameters. In the case of the relay channel with a single relay as well as the two-relay Gaussian diamond network, the gap is 1 bit/s/Hz. Moreover, the scheme is universal in the sense that the relays need no knowledge of the values of the channel parameters to (approximately) achieve the rate supportable by the network. We also present extensions of the results to multicast networks, half-duplex networks and ergodic networks.