  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.
