A digital interface for Gaussian relay and interference networks: Lifting codes from the discrete superposition model

TL;DR

This paper demonstrates that discrete superposition networks serve as effective digital interfaces for Gaussian networks, allowing codes to be transferred with minimal rate loss, thus simplifying the design of communication strategies.

Contribution

It introduces a lifting scheme that maps codes from discrete superposition networks to Gaussian networks with a constant rate gap, applicable to various network types including relay, interference, and multicast networks.

Findings

Codes for discrete superposition networks can be lifted to Gaussian networks with a constant rate loss.

Capacities of Gaussian and discrete superposition networks are within a constant gap, independent of channel gains and SNR.

The lifting scheme applies to multiple network configurations, including MIMO and multicast networks.

Abstract

For every Gaussian network, there exists a corresponding deterministic network called the discrete superposition network. We show that this discrete superposition network provides a near-optimal digital interface for operating a class consisting of many Gaussian networks in the sense that any code for the discrete superposition network can be naturally lifted to a corresponding code for the Gaussian network, while achieving a rate that is no more than a constant number of bits lesser than the rate it achieves for the discrete superposition network. This constant depends only on the number of nodes in the network and not on the channel gains or SNR. Moreover the capacities of the two networks are within a constant of each other, again independent of channel gains and SNR. We show that the class of Gaussian networks for which this interface property holds includes relay networks with a single source-destination pair, interference networks, multicast networks, and the counterparts of these networks with multiple transmit and receive antennas. The code for the Gaussian relay network can be obtained from any code for the discrete superposition network simply by pruning it. This lifting scheme establishes that the superposition model can indeed potentially serve as a strong surrogate for designing codes for Gaussian relay networks. We present similar results for the K x K Gaussian interference network, MIMO Gaussian interference networks, MIMO Gaussian relay networks, and multicast networks, with the constant gap depending additionally on the number of antennas in case of MIMO networks.