Coding Schemes and Asymptotic Capacity of the Gaussian Broadcast and Interference Channels with Feedback

TL;DR

This paper investigates the capacity and coding schemes for Gaussian broadcast and interference channels with feedback, revealing conditions under which feedback provides unbounded or bounded rate gains, especially with correlated noises.

Contribution

It introduces a coding scheme for Gaussian broadcast channels with correlated noises and feedback, analyzing capacity gains under various noise correlations and feedback conditions.

Findings

Sum-rate gap vanishes at high SNR for all noise correlations except -1.

Unbounded feedback gains occur when noise correlation is -1 with perfect feedback.

Feedback is ineffective if noise correlation is +1 and variances are equal.

Abstract

A coding scheme is proposed for the memoryless Gaussian broadcast channel with correlated noises and feedback. For all noise correlations other than -1, the gap between the sum-rate the scheme achieves and the full-cooperation bound vanishes as the signal-to-noise ratio tends to infinity. When the correlation coefficient is -1, the gains afforded by feedback are unbounded and the prelog is doubled. When the correlation coefficient is +1 we demonstrate a dichotomy: If the noise variances are equal, then feedback is useless, and otherwise, feedback affords unbounded rate gains and doubles the prelog. The unbounded feedback gains, however, require perfect (noiseless) feedback. When the feedback links are noisy the feedback gains are bounded, unless the feedback noise decays to zero sufficiently fast with the signal-to-noise ratio. Extensions to more receivers are also discussed as is the memoryless Gaussian interference channel with feedback.