On the Noisy Feedback Capacity of Gaussian Broadcast Channels

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.Comment: 5 pages, 3 figures, to appear in IEEE Information Theory Workshop 2015, Jerusale

Capacity of All Nine Models of Channel Output Feedback for the Two-user Interference Channel

In this paper, we study the impact of different channel output feedback architectures on the capacity of the two-user interference channel. For a two-user interference channel, a feedback link can exist between receivers and transmitters in 9 canonical architectures (see Fig. 2), ranging from only one feedback link to four feedback links. We derive the exact capacity region for the symmetric deterministic interference channel and the constant-gap capacity region for the symmetric Gaussian interference channel for all of the 9 architectures. We show that for a linear deterministic symmetric interference channel, in the weak interference regime, all models of feedback, except the one, which has only one of the receivers feeding back to its own transmitter, have the identical capacity region. When only one of the receivers feeds back to its own transmitter, the capacity region is a strict subset of the capacity region of the rest of the feedback models in the weak interference regime. However, the sum-capacity of all feedback models is identical in the weak interference regime. Moreover, in the strong interference regime all models of feedback with at least one of the receivers feeding back to its own transmitter have the identical sum-capacity. For the Gaussian interference channel, the results of the linear deterministic model follow, where capacity is replaced with approximate capacity.Comment: submitted to IEEE Transactions on Information Theory, results improved by deriving capacity region of all 9 canonical feedback models in two-user interference channe

Dependence Balance Based Outer Bounds for Gaussian Networks with Cooperation and Feedback

We obtain new outer bounds on the capacity regions of the two-user multiple access channel with generalized feedback (MAC-GF) and the two-user interference channel with generalized feedback (IC-GF). These outer bounds are based on the idea of dependence balance which was proposed by Hekstra and Willems [1]. To illustrate the usefulness of our outer bounds, we investigate three different channel models. We first consider a Gaussian MAC with noisy feedback (MAC-NF), where transmitter $k$, $k=1,2$, receives a feedback $Y_{F_{k}}$, which is the channel output $Y$ corrupted with additive white Gaussian noise $Z_{k}$. As the feedback noise variances become large, one would expect the feedback to become useless, which is not reflected by the cut-set bound. We demonstrate that our outer bound improves upon the cut-set bound for all non-zero values of the feedback noise variances. Moreover, in the limit as $\sigma_{Z_{k}}^{2}\to \infty$, $k=1,2$, our outer bound collapses to the capacity region of the Gaussian MAC without feedback. Secondly, we investigate a Gaussian MAC with user-cooperation (MAC-UC), where each transmitter receives an additive white Gaussian noise corrupted version of the channel input of the other transmitter [2]. For this channel model, the cut-set bound is sensitive to the cooperation noises, but not sensitive enough. For all non-zero values of cooperation noise variances, our outer bound strictly improves upon the cut-set outer bound. Thirdly, we investigate a Gaussian IC with user-cooperation (IC-UC). For this channel model, the cut-set bound is again sensitive to cooperation noise variances but not sensitive enough. We demonstrate that our outer bound strictly improves upon the cut-set bound for all non-zero values of cooperation noise variances.Comment: Submitted to IEEE Transactions on Information Theor