Martina Cardone

Gaussian Half-Duplex Relay Networks: Improved Constant Gap and Connections With the Assignment Problem

This paper considers a Gaussian relay network where a source transmits a message to a destination with the help of N half-duplex relays. The information theoretic cut-set upper bound to the capacity is shown to be achieved to within 1.96(N+2) bits by noisy network coding, thereby reducing the previously known gap. This gap is obtained as a special case of a more general constant gap result for Gaussian half-duplex multicast networks. It is then shown that the generalized degrees-of-freedom of this network is the solution of a linear program, where the coefficients of the linear inequality constraints are proved to be the solution of several linear programs referred as the assignment problem in graph theory, for which efficient numerical algorithms exist. The optimal schedule, that is, the optimal value of the 2N possible transmit-receive configuration states for the relays, is investigated and known results for diamond networks are extended to general relay networks. It is shown, for the case of N=2 relays, that only N+1=3 out of the 2N=4 possible states have a strictly positive probability and suffice to characterize the capacity to within a constant gap. Extensive experimental results show that, for a general N -relay network with N≤8 , the optimal schedule has at most N+1 states with a strictly positive probability. As an extension of a conjecture presented for diamond networks, it is conjectured that this result holds for any half-duplex relay network and any number of relays. Finally, a network with N=2 relays is studied in detail to illustrate the channel conditions under which selecting the best relay is not optimal, and to highlight the nature of the rate gain due to multiple relays.

On the Gaussian Half-Duplex Relay Channel

This paper considers the Gaussian half-duplex relay channel (G-HD-RC): a channel model where a source transmits a message to a destination with the help of a relay that cannot transmit and receive at the same time. It is shown that the cut-set upper bound on the capacity can be achieved to within a constant gap, regardless of the actual value of the channel parameters, by either partial-decode-and-forward or compress-and-forward. The performance of these coding strategies is evaluated with both random and deterministic switch at the relay. Numerical evaluations show that the actual gap is less than what analytically obtained, and that random switch achieves higher rates than deterministic switch. As a result of this analysis, the generalized degrees-of-freedom of the G-HD-RC is exactly characterized for this channel. In order to get insights into practical schemes for the G-HD-RC that are less complex than partial-decode-and-forward or compress-and-forward, the exact capacity of the linear deterministic approximation (LDA) of the G-HD-RC at high signal-to-noise-ratio is determined. It is shown that random switch and correlated nonuniform inputs bits are optimal for the LDA. It is then demonstrated that deterministic switch is to within one bit from the capacity. This latter scheme is translated into a coding strategy for the original G-HD-RC and its optimality to within a constant gap is proved. The gap attained by this scheme is larger than that of partial-decode-and-forward, thereby pointing to an interesting practical tradeoff between gap to capacity and complexity.

SINR balancing and beamforming for the MISO interference channel

In this paper a K user multi-input single-output (MISO) interference channel (IFC) is considered where the interference at each receiver is treated as an additional Gaussian noise contribution (Noisy IFC). We address the MISO downlink (DL) beamformer design and power allocation for maximizing the minimum SINR with per base station power constraints and imposing a minimum quality of service (QoS) requirement for each receiver. We study a distributed iterative algorithm for solving the given beamforming problem based on a combination of duality principles and the property that maxmin SINR problem is strictly related to the total power minimization problem. Finally we show that it is possible to characterize the entire Pareto boundary of the SINR (Rate) region for a K-user MISO IFC solving a sequence of maxmin SINR imposing different set of QoS constraints.

On the Capacity of the Two-User Gaussian Causal Cognitive Interference Channel

This paper considers the two-user Gaussian causal cognitive interference channel (GCCIC), which consists of two source-destination pairs that share the same channel and where one full-duplex cognitive source can causally learn the message of the primary source through a noisy link. The GCCIC is an interference channel with unilateral source cooperation that better models practical cognitive radio networks than the commonly used model which assumes that one source has perfect noncausal knowledge of the other sources message. First, the sum-capacity of the symmetric GCCIC is determined to within a constant gap. Then, the insights gained from the study of the symmetric GCCIC are extended to more general cases. In particular, the whole capacity region of the Gaussian Z-channel, i.e., when there is no interference from the primary user, and of the Gaussian S-channel, i.e., when there is no interference from the secondary user, are both characterized to within 2 bits. The fully connected general, i.e., no-symmetric, GCCIC is also considered and its capacity region is characterized to within 2 bits when, roughly speaking, the interference is not weak at both receivers. The parameter regimes where the GCCIC is equivalent, in terms of generalized degrees-of-freedom, to the noncooperative interference channel (i.e., unilateral causal cooperation is not useful), to the non-causal cognitive interference channel (i.e., causal cooperation attains the ultimate limit of cognitive radio technology), and to bilateral source cooperation are identified. These comparisons shed light into the parameter regimes and network topologies that in practice might provide an unbounded throughput gain compared to currently available (non cognitive) technologies.

The approximate optimality of simple schedules for half-duplex multi-relay networks

In ISIT2012 Brahma, Özgür and Fragouli conjectured that in a half-duplex diamond relay network (a Gaussian noise network without a direct source-destination link and with N non-interfering relays) an approximately optimal relay scheduling (achieving the cut-set upper bound to within a constant gap uniformly over all channel gains) exists with at most N + 1 active states (only N + 1 out of the 2N possible relay listen-transmit configurations have a strictly positive probability). Such relay scheduling policies are said to be simple. In ITW2013 we conjectured that simple relay policies are optimal for any half-duplex Gaussian multi-relay network, that is, simple schedules are not a consequence of the diamond networks sparse topology. In this paper we formally prove the conjecture beyond Gaussian networks. In particular, for any memoryless half-duplex N-relay network for which the cut-set bound is approximately optimal to within a constant gap under some conditions (satisfied for example by Gaussian networks), an optimal schedule exists with at most N + 1 active states. The key step of our proof is to write the minimum of a submodular function by means of its Lovász extension and use the greedy algorithm for submodular polyhedra to highlight structural properties of the optimal solution. This, together with the saddle-point property of min-max problems and the existence of optimal basic feasible solutions in linear programs, proves the claim.

New outer bounds for the interference channel with unilateral source cooperation

This paper studies the two-user interference channel with unilateral source cooperation, which consists of two source-destination pairs that share the same channel and where one full-duplex source can overhear the other source through a noisy in-band link. Novel outer bounds of the type 2R1 + R2 and R1 + 2R2 are developed for the class of injective semi-deterministic channels with independent noises at the different source-destination pairs. The bounds are then specialized to the Gaussian noise case. Interesting insights are provided about when these types of bounds are active, or in other words, when unilateral cooperation is too weak and leaves some system resources underutilized.

Gaussian half-duplex relay channels: Generalized degrees of freedom and constant gap result

This paper considers the Gaussian relay channel where the relay node operates in half-duplex mode. The exact capacity of the linear deterministic approximation of the Gaussian channel at high SNR is derived first. This result is then used to inspire an achievable scheme valid for any SNR in the original channel. The scheme is quite simple: it uses successive decoding and does not incur in the typical delay of backward decoding. The achievable rate is then showed to be at most 3 bits away from the cut-set upper bound, which allows to analytically determine the generalized Degrees-of-Freedom of the channel. A closed form expression for the gDoF-optimal fraction of time the relay node transmits is found as well.

The capacity to within a constant gap of the Gaussian half-duplex relay channel

This paper studies the Gaussian half duplex relay channel, where the relay node can not transmit and receive at the same time. The main contribution lies in showing that both Partial-Decode-Forward and Compress-Forward achieve the CutSet upper bound to within a constant gap regardless of the channel parameters. This provides a closed form characterization of the Generalized Degrees-of-Freedom (gDoF) of the channel, which for certain channel parameters is strictly smaller than the gDoF of the full duplex channel. Half duplex channels can convey information through the random switch between the receive and retransmit phases; this work shows numerically that random switch achieves larger rates compared to deterministic switch, which is usually considered in the literature.

Coding across unicast sessions can increase the secure message capacity

This paper characterizes the secret message capacity of three networks where two unicast sessions share some of the communication resources. Each network consists of erasure channels with state feedback. A passive eavesdropper is assumed to wiretap any one of the links. The capacity achieving schemes as well as the outer bounds are formulated as linear programs. The proposed strategies are then numerically evaluated and shown to achieve higher rate performances (up to a double single- or sum-rate) with respect to alternative strategies, where the network resources are time-shared among the two sessions. These results represent a step towards the secure capacity characterization for general networks. They also show that, even in configurations for which network coding does not offer benefits in absence of security, it can become beneficial under security constraints.

On the capacity of full-duplex causal cognitive interference channels to within a constant gap

This paper considers the two-user Gaussian Causal Cognitive Interference Channel (GCCIC), which consists of two source-destination pairs that share the same channel and where one full-duplex cognitive source can causally learn the message of the primary source through a noisy link. The GCCIC is an interference channel with unilateral source cooperation that models practical cognitive radio networks. Different achievable strategies are shown to be at most a finite number of bits away from an outer bound for a set of the channel parameters that, roughly speaking, excludes the case of weak interference at both receivers.