  Motivated by the design of low-complexity low-power coding solutions for the
Gaussian relay channel, this work presents an upper bound on the minimum
energy-per-bit achievable on the Gaussian relay channel using rank-1 linear
relaying. Our study addresses high-dimensional relay codes and presents bounds
that outperform prior known bounds using 2-dimensional schemes. A novelty of
our analysis ties the optimization problem at hand to the solution of a certain
differential equation which, in turn, leads to a low energy-per-bit achievable
scheme.
