A digital interface for Gaussian relay networks: lifting codes from the discrete superposition model to Gaussian relay networks

TL;DR

This paper proves that coding schemes designed for discrete superposition models can be effectively transferred to Gaussian relay networks with only a bounded, constant rate loss, regardless of SNR, making the former a practical digital interface.

Contribution

It establishes that codes for discrete superposition networks can be lifted to Gaussian relay networks with a bounded, SNR-independent rate loss, enabling practical code design.

Findings

Codes for discrete superposition networks can be pruned for Gaussian networks.

Rate loss in Gaussian networks is bounded by a constant depending on network size.

Applicable to MIMO Gaussian relay networks with additional antenna considerations.

Abstract

For every Gaussian relay network with a single source-destination pair, it is known that there exists a corresponding deterministic network called the discrete superposition network that approximates its capacity uniformly over all SNR's to within a bounded number of bits. The next step in this program of rigorous approximation is to determine whether coding schemes for discrete superposition models can be lifted to Gaussian relay networks with a bounded rate loss independent of SNR. We establish precisely this property and show that the superposition model can thus serve as a strong surrogate for designing codes for Gaussian relay networks. We show that a code for a Gaussian relay network, with a single source-destination pair and multiple relay nodes, can be designed from any code for the corresponding discrete superposition network simply by pruning it. In comparison to the rate of the discrete superposition network's code, the rate of the Gaussian network's code only reduces at most by a constant that is a function only of the number of nodes in the network and independent of channel gains. This result is also applicable for coding schemes for MIMO Gaussian relay networks, with the reduction depending additionally on the number of antennas. Hence, the discrete superposition model can serve as a digital interface for operating Gaussian relay networks.