Oblivious Fronthaul-Constrained Relay for a Gaussian Channel

Abstract

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 also to a MIMO transmission scheme. We also investigate the case of an entropy-limited relay. We show that the optimal relay function is always deterministic, present lower and upper bounds on the optimal performance (in terms of mutual information), and derive an analytical approximation.

Gaussian Diamond Primitive Relay with Oblivious Processing

“…In this method, that was shown in [5] and [6], we split the channel into separate bands, each with bandwidth of df. In our Gaussian model, the different bands are independent.…”

“…A single relay scheme and the optimal frequencydependent allocation of power and bitrate was investigated in [5], [6] using Gaussian bottleneck results [7] and Shannon's incremental frequency approach [8]. The problem can be compared to the remote source coding, only with logarithmic loss instead of mean square error in [9] The scheme for this relay is shown in [5,Fig.…”

On the Information Bottleneck Problems: Models, Connections, Applications and Information Theoretic Views

“…The solution of this problem turns out to be a deterministic encoder map as opposed to the stochastic encoder map that is optimal under the IB framework of Tishby et al [ 1 ], which results in a reduction of the algorithm’s complexity. This idea was then used and extended to the case of available resource (or time) sharing in [ 108 ].…”

“…It is conjectured that the optimal input distribution is discrete. Other issues might relate to extensions to continuous time filtered Gaussian channels, in parallel to the regular bottleneck problem [ 108 ], or extensions to settings in which fronthauls may be not available at some radio-units, and that is unknown to the systems. That is, the more radio units are connected to the central unit, the higher is the rate that could be conveyed over the CRAN uplink [ 110 ].…”

Uplink Oblivious Cloud Radio Access Networks: An Information Theoretic Overview

“…It is conjectured that the optimal input distribution is discrete. Other issues might relate to extensions to continuous time filtered Gaussian channels, in parallel to the regular bottleneck problem [24], or extensions to settings in which fronthauls may be not available at some radio-units, and that is unknown to the systems. That is, the more radio units are connected to the central unit the higher rate could be conveyed over the CRAN uplink [25].…”