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

Optimal WiFi Sensing via Dynamic Programming

The problem of finding an optimal sensing schedule for a mobile device that encounters an intermittent WiFi access opportunity is considered. At any given time, the WiFi is in any of the two modes, ON or OFF, and the mobile's incentive is to connect to the WiFi in the ON mode as soon as possible, while spending as little sensing energy. We introduce a dynamic programming framework which enables the characterization of an explicit solution for several models, particularly when the OFF periods are exponentially distributed. While the problem for non-exponential OFF periods is ill-posed in general, a usual workaround in literature is to make the mobile device aware if one ON period is completely missed. In this restricted setting, using the DP framework, the deterministic nature of the optimal sensing policy is established, and value iterations are shown to converge to the optimal solution. Finally, we address the blind situation where the distributions of ON and OFF periods are unknown. A continuous bandit based learning algorithm that has vanishing regret (loss compared to the optimal strategy with the knowledge of distributions) is presented, and comparisons with the optimal schemes are provided for exponential ON and OFF times

Multiple Access Channel Simulation

We study the problem of simulating a two-user multiple access channel over a multiple access network of noiseless links. Two encoders observe independent and identically distributed (i.i.d.) copies of a source random variable each, while a decoder observes i.i.d. copies of a side-information random variable. There are rate-limited noiseless communication links and independent pairwise shared randomness resources between each encoder and the decoder. The decoder has to output approximately i.i.d. copies of another random variable jointly distributed with the two sources and the side information. We are interested in the rate tuples which permit this simulation. This setting can be thought of as a multi-terminal generalization of the point-to-point channel simulation problem studied by Bennett et al. (2002) and Cuff (2013). General inner and outer bounds on the rate region are derived. For the specific case where the sources at the encoders are conditionally independent given the side-information at the decoder, we completely characterize the rate region. Our bounds recover the existing results on function computation over such multi-terminal networks. We then show through an example that an additional independent source of shared randomness between the encoders strictly improves the communication rate requirements, even if the additional randomness is not available to the decoder. Furthermore, we provide inner and outer bounds for this more general setting with independent pairwise shared randomness resources between all the three possible node pairs.Comment: 33 pages, 3 figure