Aly El Gamal

Achievable Secrecy Rate Regions for the Two-Way Wiretap Channel

The two-way wiretap channel is considered in this paper. Two legitimate users, Alice and Bob, wish to exchange messages securely in the presence of a passive eavesdropper Eve. In the full-duplex scenario, where each node can transmit and receive simultaneously, new achievable secrecy rate regions are obtained based on the idea of allowing the two users to jointly optimize their channel prefixing distributions and binning codebooks in addition to key sharing. The new regions are shown to be strictly larger than the known ones for a wide class of discrete memoryless and Gaussian channels. In the half-duplex case, where a user can only transmit or receive on any given degree of freedom, the idea of randomized scheduling is introduced and shown to offer a significant gain in terms of the achievable secrecy sum-rate. A practical setup is further developed based on a near field wireless communication scenario, and it is shown that one can exploit the two-way nature of the communication, via appropriately randomizing the transmit power levels and transmission schedule, to introduce significant ambiguity at a noiseless Eve.

Interference Channels With Coordinated Multipoint Transmission: Degrees of Freedom, Message Assignment, and Fractional Reuse

Coordinated multipoint (CoMP) transmission is an infrastructural enhancement under consideration for next generation wireless networks. In this paper, the capacity gain achieved through CoMP transmission is studied in various models of wireless networks that have practical significance. The capacity gain is analyzed through the degrees of freedom (DoF) criterion. The DoF available for communication provides an analytically tractable way to characterize the capacity of interference channels. The considered channel model has K transmitter/receiver pairs, and each receiver is interested in one unique message from a set of K independent messages. Each message can be available at more than one transmitter. The maximum number of transmitters at which each message can be available, is defined as the cooperation order M. For fully connected interference channels, it is shown that the asymptotic per user DoF, as K goes to infinity, remains at 1/2 as M is increased from 1 to 2. Furthermore, the same negative result is shown to hold for all M ≥ 2 for any message assignment that satisfies a local cooperation constraint. On the other hand, when the assumption of full connectivity is relaxed to local connectivity, and each transmitter is connected only to its own receiver as well as L neighboring receivers, it is shown that local cooperation is optimal. The asymptotic per user DoF is shown to be at least max {1/2, 2M/(2M + L)} for locally connected channels, and is shown to be 2M/(2M + 1) for the special case of Wyners asymmetric model where L = 1. An interesting feature of the proposed achievability scheme is that it relies on simple zero-forcing transmit beams and does not require symbol extensions. Also, to achieve the optimal per user DoF for Wyners model, messages are assigned to transmitters in an asymmetric fashion unlike traditional assignments where message i has to be available at transmitter i. It is also worth noting that some receivers have to be inactive, and fractional reuse is needed to achieve equal DoF for all users.

When does an ensemble of matrices with randomly scaled rows lose rank

We consider the problem of determining rank loss conditions for a concatenation of full-rank matrices, such that each row of the composing matrices is scaled by a random coefficient. This problem has applications in wireless interference management and recommendation systems. We determine necessary and sufficient conditions for the design of each matrix, such that the random ensemble will almost surely lose rank by a certain amount. The result is proved by converting the problem to determining rank loss conditions for the union of some specific matroids, and then using tools from matroid and graph theories to derive the necessary and sufficient conditions. As an application, we discuss how this result can be applied to the problem of topological interference management, and characterize the linear symmetric degrees of freedom for a class of network topologies.

Degrees of freedom (DoF) of locally connected interference channels with coordinated multi-point (CoMP) transmission

The degrees of freedom (DoF) available for communication provides an analytically tractable way to characterize the information-theoretic capacity of interference channels. In this paper, the DoF of a K-user interference channel is studied under the assumption that the transmitters can cooperate via coordinated multi-point (CoMP) transmission. In [1], the authors considered the linear asymmetric model of Wyner, where each transmitter is connected to its own receiver and its successor, and is aware of its own message as well as M - 1 preceding messages. The per user DoF was shown to go to M/M+1 as the number of users increases to infinity. In this work, the same model of channel connectivity is considered, with a relaxed cooperation constraint that bounds the maximum number of transmitters at which each message can be available, by a cooperation order M. We show that the relaxation of the cooperation constraint, while maintaining the same load imposed on a backhaul link needed to distribute the messages, results in a gain in the DoF. In particular, the asymptotic limit of the per user DoF under the cooperation order constraint is 2M/2M+1. Moreover, the optimal transmit set selection satisfies a local cooperation constraint. i.e., each message needs only to be available at neighboring transmitters.

New achievable secrecy rate regions for the two way wiretap channel

1 This work develops new achievable rate regions for the two way wiretap channel. In our setup, Alice and Bob wish to exchange messages securely in the presence of a passive eavesdropper Eve. In the full-duplex scenario, our achievability argument relies on allowing the two users to jointly optimize their channel prefixing distributions, such that the new channel conditions are favorable compared to that of Eve. Random binning and private key sharing over the channel are then used to exploit the secrecy advantage available in the equivalent cascade channel and to distribute the available secrecy rate among users. For the half-duplex case, we introduce the idea of randomized scheduling and establish the significant gain it offers in terms of the achievable secrecy sum-rate. We also quantify the gains that can be leveraged from the proposed schemes in the modulo-2 and Gaussian channels via numerical results in certain selected scenarios.

Dynamic interference management

A linear interference network is considered. Long-term fluctuations (shadow fading) in the wireless channel can lead to any link being erased with probability p. Each receiver is interested in one unique message that can be available at M transmitters. In a cellular downlink scenario, the case where M = 1 reflects the cell association problem, and the case where M > 1 reflects the problem of setting up the backhaul links for Coordinated Multi-Point (CoMP) transmission. For M = 1, we characterize the average per user DoF, and identify the optimal assignment of messages to transmitters at each value of p. For general values of M, we show that there is no strategy for assigning messages to transmitters in large networks that is optimal for all values of p.

Degrees of freedom of the K-user interference channel with transmitter cooperation

We consider the K-user Gaussian interference channel in the context of the downlink of a cellular system where the base stations can exchange messages through a backhaul network, and the interfering users can be jointly served by multiple base stations. To limit the load on the backhaul network, the number of (base station) transmitters sharing a given message is bounded by a number M, which we call the cooperation order. We provide outer bounds on the sum degrees of freedom of this system, which are shown to be tight in special cases.

Flexible backhaul design with cooperative transmission in cellular interference networks

We propose a novel interference management framework for the cellular downlink through cooperative transmission. A sectored cellular network is studied where the interference is only due to sectors in neighboring cells and intra cell interference is ignored. We first explore the potential degrees of freedom (DoF) gain in a scenario where mobile receivers can be associated to any neighboring cell but no cooperative transmission is allowed. We show that the maximum achievable per user DoF for orthogonal schemes is between 1/3 and 3/7. On the other hand, if cooperative transmission is combined with flexible message assignment to the transmitters, we show that it is possible to achieve a per user DoF of 7/15. In addition, the proposed cooperative transmission scheme does not require extra backhaul capacity, as it uses a smart assignment of messages to transmitters to meet an average backhaul load constraint of one message per transmitter.

Asymptotic justification of bandlimited interpolation of graph signals for semi-supervised learning

Graph-based methods play an important role in unsupervised and semi-supervised learning tasks by taking into account the underlying geometry of the data set. In this paper, we consider a statistical setting for semi-supervised learning and provide a formal justification of the recently introduced framework of bandlimited interpolation of graph signals. Our analysis leads to the interpretation that, given enough labeled data, this method is very closely related to a constrained low density separation problem as the number of data points tends to infinity. We demonstrate the practical utility of our results through simple experiments.

Flexible backhaul design and degrees of freedom for linear interference networks

The considered problem is that of maximizing the degrees of freedom (DoF) in cellular downlink, under a backhaul load constraint that limits the number of messages that can be delivered from a centralized controller to the base station transmitters. A linear interference channel model is considered, where each transmitter is connected to the receiver having the same index as well as one succeeding receiver. The backhaul load is defined as the sum of all the messages available at all the transmitters normalized by the number of users. When the backhaul load is constrained to an integer level B, the asymptotic per user DoF is shown to equal equation, and it is shown that the optimal assignment of messages to transmitters is asymmetric and satisfies a local cooperation constraint and that the optimal coding scheme relies only on zero-forcing transmit beamforming. Finally, an extension of the presented coding scheme for the case where B = 1 is shown to apply for more general locally connected and two-dimensional networks.