On the Dirty Paper Channel with Fast Fading Dirt

Costa`s "writing on dirty paper" result establishes that full state pre-cancellation can be attained in the Gel`fand-Pinsker problem with additive state and additive white Gaussian noise. This result holds under the assumptions that full channel knowledge is available at both the transmitter and the receiver. In this work we consider the scenario in which the state is multiplied by an ergodic fading process which is not known at the encoder. We study both the case in which the receiver has knowledge of the fading and the case in which it does not: for both models we derive inner and outer bounds to capacity and determine the distance between the two bounds when possible. For the channel without fading knowledge at either the transmitter or the receiver, the gap between inner and outer bounds is finite for a class of fading distributions which includes a number of canonical fading models. In the capacity approaching strategy for this class, the transmitter performs Costa`s pre-coding against the mean value of the fading times the state while the receiver treats the remaining signal as noise. For the case in which only the receiver has knowledge of the fading, we determine a finite gap between inner and outer bounds for two classes of discrete fading distribution. The first class of distributions is the one in which there exists a probability mass larger than one half while the second class is the one in which the fading is uniformly distributed over values that are exponentially spaced apart. Unfortunately, the capacity in the case of a continuous fading distribution remains very hard to characterize

On the Information Bottleneck Problems: An Information Theoretic Perspective

International Zurich Seminar on Information and Communication (IZS), February 26 – 28, 202

Mixed Delay Constraints at Maximum Sum-Multiplexing Gain

International audienceCoding schemes are proposed for Wyner's soft-handoff model and for the sectorized hexagonal model when some of the messages are delay-sensitive and cannot profit from transmitter or receiver cooperation. For the soft-handoff network we also provide a converse. It matches the multiplexing-gain achieved by our scheme when the multiplexing gain of the delay-sensitive messages is low or moderate or when the cooperation links have high capacities. In these cases, the sum-multiplexing gain is the same as if only delay-tolerant messages (which can profit from cooperation) were sent. A similar conclusion holds for the sectorized hexagonal model, when the capacities of the cooperation links are large

A Broadcast Approach for Fading Wiretap Channels

A (layered) broadcast approach is studied for the fading wiretap channel without the channel state information (CSI) at the transmitter. Two broadcast schemes, based on superposition coding and embedded coding respectively, are developed to encode information into a number of layers and use stochastic encoding to keep the corresponding information secret from an eavesdropper. The layers that can be successfully and securely transmitted are determined by the channel states to the legitimate receiver and the eavesdropper. The advantage of these broadcast approaches is that the transmitter does not need to know the CSI to the legitimate receiver and the eavesdropper, but the scheme still adapts to the channel states of the legitimate receiver and the eavesdropper. Three scenarios of block fading wiretap channels with a stringent delay constraint are studied, in which either the legitimate receiver’s channel, the eavesdropper’s channel, or both channels are fading. For each scenario, the secrecy rate that can be achieved via the broadcast approach developed in this paper is derived, and the optimal power allocation over the layers (or the conditions on the optimal power allocation) is also characterized. A notion of probabilistic secrecy is also introduced and studied for scenarios when the eavesdropper’s channel is fading, which characterizes the probability that a certain secrecy rate of decoded messages is achieved during one block. Numerical examples are provided to demonstrate the impact of the channel state information at the transmitter and the channel fluctuation of the eavesdropper on the average secrecy rate. These examples also demonstrate the advantage of the proposed broadcast approach over the compound channel approach

Secure Degrees of Freedom of MIMO X-Channels with Output Feedback and Delayed CSIT

We investigate the problem of secure transmission over a two-user multi-input multi-output (MIMO) X-channel in which channel state information is provided with one-unit delay to both transmitters (CSIT), and each receiver feeds back its channel output to a different transmitter. We refer to this model as MIMO X-channel with asymmetric output feedback and delayed CSIT. The transmitters are equipped with M-antennas each, and the receivers are equipped with N-antennas each. For this model, accounting for both messages at each receiver, we characterize the optimal sum secure degrees of freedom (SDoF) region. We show that, in presence of asymmetric output feedback and delayed CSIT, the sum SDoF region of the MIMO X-channel is same as the SDoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver and delayed CSIT. This result shows that, upon availability of asymmetric output feedback and delayed CSIT, there is no performance loss in terms of sum SDoF due to the distributed nature of the transmitters. Next, we show that this result also holds if only output feedback is conveyed to the transmitters, but in a symmetric manner, i.e., each receiver feeds back its output to both transmitters and no CSIT. We also study the case in which only asymmetric output feedback is provided to the transmitters, i.e., without CSIT, and derive a lower bound on the sum SDoF for this model. Furthermore, we specialize our results to the case in which there are no security constraints. In particular, similar to the setting with security constraints, we show that the optimal sum DoF region of the (M,M,N,N)--MIMO X-channel with asymmetric output feedback and delayed CSIT is same as the DoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver, and delayed CSIT. We illustrate our results with some numerical examples.Comment: To Appear in IEEE Transactions on Information Forensics and Securit

Throughput Scaling of Wireless Networks With Random Connections

This work studies the throughput scaling laws of ad hoc wireless networks in the limit of a large number of nodes. A random connections model is assumed in which the channel connections between the nodes are drawn independently from a common distribution. Transmitting nodes are subject to an on-off strategy, and receiving nodes employ conventional single-user decoding. The following results are proven: 1) For a class of connection models with finite mean and variance, the throughput scaling is upper-bounded by $O(n^{1/3})$ for single-hop schemes, and $O(n^{1/2})$ for two-hop (and multihop) schemes. 2) The $\Theta (n^{1/2})$ throughput scaling is achievable for a specific connection model by a two-hop opportunistic relaying scheme, which employs full, but only local channel state information (CSI) at the receivers, and partial CSI at the transmitters. 3) By relaxing the constraints of finite mean and variance of the connection model, linear throughput scaling $\Theta (n)$ is achievable with Pareto-type fading models.Comment: 13 pages, 4 figures, To appear in IEEE Transactions on Information Theor