Partial Strong Converse for the Non-Degraded Wiretap Channel

We prove the partial strong converse property for the discrete memoryless \emph{non-degraded} wiretap channel, for which we require the leakage to the eavesdropper to vanish but allow an asymptotic error probability $\epsilon \in [0,1)$ to the legitimate receiver. We show that when the transmission rate is above the secrecy capacity, the probability of correct decoding at the legitimate receiver decays to zero exponentially. Therefore, the maximum transmission rate is the same for $\epsilon \in [0,1)$, and the partial strong converse property holds. Our work is inspired by a recently developed technique based on information spectrum method and Chernoff-Cramer bound for evaluating the exponent of the probability of correct decoding

Vector Broadcast Channels: Optimality of Threshold Feedback Policies

Beamforming techniques utilizing only partial channel state information (CSI) has gained popularity over other communication strategies requiring perfect CSI thanks to their lower feedback requirements. The amount of feedback in beamforming based communication systems can be further reduced through selective feedback techniques in which only the users with channels good enough are allowed to feed back by means of a decentralized feedback policy. In this paper, we prove that thresholding at the receiver is the rate-wise optimal decentralized feedback policy for feedback limited systems with prescribed feedback constraints. This result is highly adaptable due to its distribution independent nature, provides an analytical justification for the use of threshold feedback policies in practical systems, and reinforces previous work analyzing threshold feedback policies as a selective feedback technique without proving its optimality. It is robust to selfish unilateral deviations. Finally, it reduces the search for rate-wise optimal feedback policies subject to feedback constraints from function spaces to a finite dimensional Euclidean space.Comment: Submitted to IEEE International Symposium on Information Theory, St. Petersburg, Russia, Aug 201

On Continuous-Time Gaussian Channels

A continuous-time white Gaussian channel can be formulated using a white Gaussian noise, and a conventional way for examining such a channel is the sampling approach based on the Shannon-Nyquist sampling theorem, where the original continuous-time channel is converted to an equivalent discrete-time channel, to which a great variety of established tools and methodology can be applied. However, one of the key issues of this scheme is that continuous-time feedback and memory cannot be incorporated into the channel model. It turns out that this issue can be circumvented by considering the Brownian motion formulation of a continuous-time white Gaussian channel. Nevertheless, as opposed to the white Gaussian noise formulation, a link that establishes the information-theoretic connection between a continuous-time channel under the Brownian motion formulation and its discrete-time counterparts has long been missing. This paper is to fill this gap by establishing causality-preserving connections between continuous-time Gaussian feedback/memory channels and their associated discrete-time versions in the forms of sampling and approximation theorems, which we believe will play important roles in the long run for further developing continuous-time information theory. As an immediate application of the approximation theorem, we propose the so-called approximation approach to examine continuous-time white Gaussian channels in the point-to-point or multi-user setting. It turns out that the approximation approach, complemented by relevant tools from stochastic calculus, can enhance our understanding of continuous-time Gaussian channels in terms of giving alternative and strengthened interpretation to some long-held folklore, recovering "long known" results from new perspectives, and rigorously establishing new results predicted by the intuition that the approximation approach carries

On Coding for Reliable Communication over Packet Networks

We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of previously received packets. All coding and decoding operations have polynomial complexity. We show that the scheme is capacity-achieving as long as packets received on a link arrive according to a process that has an average rate. Thus, packet losses on a link may exhibit correlation in time or with losses on other links. In the special case of Poisson traffic with i.i.d. losses, we give error exponents that quantify the rate of decay of the probability of error with coding delay. Our analysis of the scheme shows that it is not only capacity-achieving, but that the propagation of packets carrying "innovative" information follows the propagation of jobs through a queueing network, and therefore fluid flow models yield good approximations. We consider networks with both lossy point-to-point and broadcast links, allowing us to model both wireline and wireless packet networks.Comment: 33 pages, 6 figures; revised appendi