  We consider systems in which the transmitter conveys messages to the receiver
through a capacity-limited relay station. The channel between the transmitter
and the relay-station is assumed to be a frequency selective additive Gaussian
noise channel. It is assumed that the transmitter can shape the spectrum and
adapt the coding technique so as to optimize performance. The relay operation
is oblivious (nomadic transmitters), that is, the specific codebooks used are
unknown. We find the reliable information rate that can be achieved with
Gaussian signaling in this setting, and to that end, employ Gaussian bottleneck
results combined with Shannon's incremental frequency approach. We also prove
that, unlike classical water-pouring, the allocated spectrum (power and
bit-rate) of the optimal solution could frequently be discontinuous. These
results can be applied to a MIMO transmission scheme. We also investigate the
case of an entropy limited relay. We present lower and upper bounds on the
optimal performance (in terms of mutual information), and derive an analytical
approximation.
