On the Noisy Feedback Capacity of Gaussian Broadcast Channels

TL;DR

This paper investigates the impact of noisy feedback on the capacity of Gaussian broadcast channels, showing that beyond a certain noise level, feedback does not increase capacity for certain channel classes.

Contribution

It demonstrates that for some two-user Gaussian broadcast channels, noisy feedback from the stronger user does not enlarge capacity if the feedback noise exceeds a threshold.

Findings

Feedback does not enlarge capacity when feedback noise is high.

The result applies to a class of two-user Gaussian broadcast channels.

Feedback from the stronger user can be ineffective under certain noise conditions.

Abstract

It is well known that, in general, feedback may enlarge the capacity region of Gaussian broadcast channels. This has been demonstrated even when the feedback is noisy (or partial-but-perfect) and only from one of the receivers. The only case known where feedback has been shown not to enlarge the capacity region is when the channel is physically degraded (El Gamal 1978, 1981). In this paper, we show that for a class of two-user Gaussian broadcast channels (not necessarily physically degraded), passively feeding back the stronger user's signal over a link corrupted by Gaussian noise does not enlarge the capacity region if the variance of feedback noise is above a certain threshold.