Oblivious processing in a fronthaul constrained Gaussian channel

We consider systems for 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 frequency selective additive Gaussian noise channel. It is assumed that the transmitter can shape the spectrum and adapt the coding technique as to optimize performance. The relay operation is oblivious(nomadic transmitters [1] ), that is, the specific codebooks used are unknown, while the spectral shape of the transmitted signal is available. We find the reliable information rate that can be achieved in this setting with Gaussian signaling, and to that end employ Gaussian bottleneck results [2] combined with Shannon's incremental frequency approach [3]. We also prove that unlike classical water-pouring, the allocated spectrum(power and bit-rate) of the optimal solution could be frequently discontinuous.