On the Capacity Enlargement of Gaussian Broadcast Channels with Passive Noisy Feedback
It is well known that the capacity region of an average transmit power constrained Gaussian Broadcast Channel (GBC) with independent noise realizations at the receivers is enlarged by the presence of causal noiseless feedback. Capacity region enlargement is also known to be possible by using only pa...
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Zusammenfassung: | It is well known that the capacity region of an average transmit power
constrained Gaussian Broadcast Channel (GBC) with independent noise
realizations at the receivers is enlarged by the presence of causal noiseless
feedback. Capacity region enlargement is also known to be possible by using
only passive noisy feedback, when the GBC has identical noise variances at the
receivers. The last fact remains true even when the feedback noise variance is
very high, and available only from one of the receivers. While such capacity
enlargements are feasible for several other feedback models in the Gaussian BC
setting, it is also known that feedback does not change the capacity region for
physically degraded broadcast channels. In this paper, we consider a two user
GBC with independent noise realizations at the receivers, where the feedback
links from the receivers are corrupted by independent additive Gaussian noise
processes. We investigate the set of four noise variances, two forward and two
feedback, for which no capacity enlargement is possible. A sharp
characterization of this region is derived, i.e., any quadruple outside the
presented region will lead to a capacity enlargement, whereas quadruples inside
will leave the capacity region unchanged. Our results lead to the conclusion
that when the forward noise variances are different, too noisy a feedback from
one of the receivers alone is not always beneficial for enlarging the capacity
region, be it from the stronger user or the weaker one, in sharp contrast to
the case of equal forward noise variances. |
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DOI: | 10.48550/arxiv.2009.08765 |