Cut-Set Bound Is Loose for Gaussian Relay Networks

TL;DR

This paper introduces a new upper bound for Gaussian relay channel capacity that is tighter than the traditional cut-set bound, showing current approximations are order-optimal and refining understanding of network capacity limits.

Contribution

We develop a novel upper bound for Gaussian relay channels that improves upon the classical cut-set bound using typicality and Gaussian measure concentration techniques.

Findings

New upper bound is tighter than the cut-set bound

Current capacity approximations are order-optimal

Provides a lower bound on the pre-constant for network capacity

Abstract

The cut-set bound developed by Cover and El Gamal in 1979 has since remained the best known upper bound on the capacity of the Gaussian relay channel. We develop a new upper bound on the capacity of the Gaussian primitive relay channel which is tighter than the cut-set bound. Our proof is based on typicality arguments and concentration of Gaussian measure. Combined with a simple tensorization argument proposed by Courtade and Ozgur in 2015, our result also implies that the current capacity approximations for Gaussian relay networks, which have linear gap to the cut-set bound in the number of nodes, are order-optimal and leads to a lower bound on the pre-constant.