arXiv subjects

Martina Cardone

Publications and source records attributed to Martina Cardone.

52 records · Page 3Linked to original sources

arXiv2017

Network Simplification in Half-Duplex: Building on Submodularity

This paper explores the {\it network simplification} problem in the context of Gaussian Half-Duplex (HD) diamond networks. Specifically, given an $N$-relay diamond network, this problem seeks to derive fundamental guarantees on the capacity of the best $k$-relay subnetwork, as a function of the full network capacity. The main focus of this work is on the case when $k=N-1$ relays are selected out of the $N$ possible ones. First, a simple algorithm, which removes the relay with the minimum capacity (i.e., the worst relay), is analyzed and it is shown that the remaining $(N-1)$-relay subnetwork has an approximate (i.e., optimal up to a constant gap) HD capacity that is at least half of the approximate HD capacity of the full network. This fraction guarantee is shown to be tight if only the single relay capacities are known, i.e., there exists a class of Gaussian HD diamond networks with $N$ relays where, by removing the worst relay, the subnetwork of the remaining $k=N-1$ relays has an approximate capacity equal to half of the approximate capacity of the full network. Next, this work proves a fundamental guarantee, which improves over the previous fraction: there always exists a subnetwork of $k=N-1$ relays that achieves at least a fraction $\frac{N-1}{N}$ of the approximate capacity of the full network. This fraction is proved to be tight and it is shown that any optimal schedule of the full network can be used by at least one of the $N$ subnetworks of $N-1$ relays to achieve a worst-case performance guarantee of $\frac{N-1}{N}$. Additionally, these results are extended to derive lower bounds on the fraction guarantee for general $k \in [1:N]$. The key steps in the proofs lie in the derivation of properties of submodular functions, which provide a combinatorial handle on the network simplification problem in Gaussian HD diamond networks.

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arXiv2017

Efficiently Finding Simple Schedules in Gaussian Half-Duplex Relay Line Networks

The problem of operating a Gaussian Half-Duplex (HD) relay network optimally is challenging due to the exponential number of listen/transmit network states that need to be considered. Recent results have shown that, for the class of Gaussian HD networks with N relays, there always exists a simple schedule, i.e., with at most N +1 active states, that is sufficient for approximate (i.e., up to a constant gap) capacity characterization. This paper investigates how to efficiently find such a simple schedule over line networks. Towards this end, a polynomial-time algorithm is designed and proved to output a simple schedule that achieves the approximate capacity. The key ingredient of the algorithm is to leverage similarities between network states in HD and edge coloring in a graph. It is also shown that the algorithm allows to derive a closed-form expression for the approximate capacity of the Gaussian line network that can be evaluated distributively and in linear time. Additionally, it is shown using this closed-form that the problem of Half-Duplex routing is NP-Hard.

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arXiv2017

Preserving Privacy while Broadcasting: $k$-Limited-Access Schemes

Index coding employs coding across clients within the same broadcast domain. This typically assumes that all clients learn the coding matrix so that they can decode and retrieve their requested data. However, learning the coding matrix can pose privacy concerns: it may enable clients to infer information about the requests and side information of other clients [1]. In this paper, we formalize the intuition that the achieved privacy can increase by decreasing the number of rows of the coding matrix that a client learns. Based on this, we propose the use of $k$-limited-access schemes: given an index coding scheme that employs $T$ transmissions, we create a $k$-limited-access scheme with $T_k\geq T$ transmissions, and with the property that each client learns at most $k$ rows of the coding matrix to decode its message. We derive upper and lower bounds on $T_k$ for all values of $k$, and develop deterministic designs for these schemes for which $T_k$ has an order-optimal exponent for some regimes.

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arXiv2017

Private Broadcasting: an Index Coding Approach

Using a broadcast channel to transmit clients' data requests may impose privacy risks. In this paper, we address such privacy concerns in the index coding framework. We show how a malicious client can infer some information about the requests and side information of other clients by learning the encoding matrix used by the server. We propose an information-theoretic metric to measure the level of privacy and show how encoding matrices can be designed to achieve specific privacy guarantees. We then consider a special scenario for which we design a transmission scheme and derive the achieved levels of privacy in closed-form. We also derive upper bounds and we compare them to the levels of privacy achieved by our scheme, highlighting that an inherent trade-off exists between protecting privacy of the request and of the side information of the clients.

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arXiv2016

On Network Simplification for Gaussian Half-Duplex Diamond Networks

This paper investigates the simplification problem in Gaussian Half-Duplex (HD) diamond networks. The goal is to answer the following question: what is the minimum (worst-case) fraction of the total HD capacity that one can always achieve by smartly selecting a subset of $k$ relays, out of the $N$ possible ones? We make progress on this problem for $k=1$ and $k=2$ and show that for $N=k+1, \ k \in \{1,2\}$ at least $\frac{k}{k+1}$ of the total HD capacity is always {approximately (i.e., up to a constant gap)} achieved. Interestingly, and differently from the Full-Duplex (FD) case, the ratio in HD depends on $N$, and decreases as $N$ increases. For all values of $N$ and $k$ for which we derive worst case fractions, we also show these to be {approximately} tight. This is accomplished by presenting $N$-relay Gaussian HD diamond networks for which the best $k$-relay subnetwork has {an approximate} HD capacity equal to the worst-case fraction of the total {approximate} HD capacity. Moreover, we provide additional comparisons between the performance of this simplification problem for HD and FD networks, which highlight their different natures.

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arXiv2016

On (Secure) Information flow for Multiple-Unicast Sessions: Analysis with Butterfly Network

This paper considers a class of wireline networks, derived from the well-known butterfly network, over which two independent unicast sessions take place simultaneously. The main objectives are to understand when network coding type of operations are beneficial with and without security considerations and to derive the ultimate gains that cooperation among sources and sinks can bring. Towards these goals, the capacity region of the butterfly network with arbitrary edge capacities is first derived. It is then shown that no rate can be guaranteed over this network under security considerations, when an eavesdropper wiretaps any of the links. Three variants of the butterfly network, such as the case of co-located sources, are analyzed as well and their secure and non-secure capacity regions are characterized. By using the butterfly network and its variants as building blocks, these results can be used to design high-throughput achieving transmission schemes for general multiple-unicast networks.

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arXiv2016

On Secure Network Coding for Two Unicast Sessions

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.

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arXiv2016

Simplifying Wireless Social Caching

Social groups give the opportunity for a new form of caching. In this paper, we investigate how a social group of users can jointly optimize bandwidth usage, by each caching parts of the data demand, and then opportunistically share these parts among themselves upon meeting. We formulate this problem as a Linear Program (LP) with exponential complexity. Based on the optimal solution, we propose a simple heuristic inspired by the bipartite set-cover problem that operates in polynomial time. Furthermore, we prove a worst case gap between the heuristic and the LP solutions. Finally, we assess the performance of our algorithm using real-world mobility traces from the MIT Reality Mining project dataset and two mobility traces that were synthesized using the SWIM model. Our heuristic performs closely to the optimal in most cases, showing a better performance with respect to alternative solutions.

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arXiv2015

The Two-user Causal Cognitive Interference Channel: Novel Outer Bounds and Constant Gap Result for the Symmetric Gaussian Noise Channel in Weak Interference

This paper studies the two-user Causal Cognitive Interference Channel (CCIC), where two transmitters aim to communicate independent messages to two different receivers via a common channel. One source, referred to as the cognitive, is capable of overhearing the other source, referred to as the primary, through a noisy in-band link and thus can assist in sending the primary's data. Two novel outer bounds of the type $2R_p+R_c$ and $R_p+2R_c$ are derived for the class of injective semi-deterministic CCICs where the noises at the different source-destination pairs are independent. An achievable rate region is derived based on Gelfand-Pinsker binning, superposition coding and simultaneous decoding at the receivers. The lower and outer bounds are then specialized to the practically relevant Gaussian noise case. The authors of this paper recently characterized to within a constant gap the capacity of the symmetric Gaussian CCIC in (a) the strong interference regime, and (b) for a subset of the weak interference regime when the cooperation link is larger than a given threshold. This work characterizes to within a constant gap the capacity for the symmetric Gaussian CCIC in the regime that was still open. In particular, it is shown that the novel outer bounds are necessary to characterize the capacity to within a constant gap when the cooperation link is weaker than the direct links, that is, in this regime unilateral cooperation leaves some system resources underutilized.

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arXiv2014

On the Optimality of Simple Schedules for Networks with Multiple Half-Duplex Relays

This paper studies networks with N half-duplex relays assisting the communication between a source and a destination. In ISIT'12 Brahma, Özgür and Fragouli conjectured that in Gaussian half-duplex diamond networks (i.e., without a direct link between the source and the destination, and with N non-interfering relays) an approximately optimal relay scheduling policy (i.e., achieving the cut-set upper bound to within a constant gap) has at most N+1 active states (i.e., at most N+1 out of the $2^N$ possible relay listen-transmit states have a strictly positive probability). Such relay scheduling policies were referred to as simple. In ITW'13 we conjectured that simple approximately optimal relay scheduling policies exist for any Gaussian half-duplex multi-relay network irrespectively of the topology. This paper formally proves this more general version of the conjecture and shows it holds beyond Gaussian noise networks. In particular, for any memoryless half-duplex N-relay network with independent noises and for which independent inputs are approximately optimal in the cut-set upper bound, an approximately optimal simple relay scheduling policy exists. A convergent iterative polynomial-time algorithm, which alternates between minimizing a submodular function and maximizing a linear program, is proposed to find the approximately optimal simple relay schedule. As an example, for N-relay Gaussian networks with independent noises, where each node in equipped with multiple antennas and where each antenna can be configured to listen or transmit irrespectively of the others, the existence of an approximately optimal simple relay scheduling policy with at most N+1 active states is proved. Through a line-network example it is also shown that independently switching the antennas at each relay can provide a strictly larger multiplexing gain compared to using the antennas for the same purpose.

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arXiv2014

The Approximate Optimality of Simple Schedules for Half-Duplex Multi-Relay Networks

In ISIT'12 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 $2^N$ possible relay listen-transmit configurations have a strictly positive probability). Such relay scheduling policies are said to be simple. In ITW'13 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 network's sparse topology. In this paper we formally prove the conjecture beyond Gaussian networks. In particular, for any memoryless half-duplex $N$-relay network with independent noises and for which independent inputs are approximately optimal in the cut-set upper bound, 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.

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arXiv2014

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 2Rp+Rc/Rp+2Rc 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 "holes" in the system resources.

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arXiv2014

On the Gaussian Interference Channel with Half-Duplex Causal Cognition

This paper studies the two-user Gaussian interference channel with half-duplex causal cognition. This channel model consists of two source-destination pairs sharing a common wireless channel. One of the sources, referred to as the cognitive, overhears the other source, referred to as the primary, through a noisy link and can therefore assist in sending the primary's data. Due to practical constraints, the cognitive source is assumed to work in half-duplex mode, that is, it cannot simultaneously transmit and receive. This model is more relevant for practical cognitive radio systems than the classical information theoretic cognitive channel model, where the cognitive source is assumed to have a non-causal knowledge of the primary's message. Different network topologies are considered, corresponding to different interference scenarios: (i) the interference-symmetric scenario, where both destinations are in the coverage area of the two sources and hence experience interference, and (ii) the interference-asymmetric scenario, where one destination does not suffer from interference. For each topology the sum-rate performance is studied by first deriving the generalized Degrees of Freedom (gDoF), or "sum-capacity pre-log" in the high-SNR regime, and then showing relatively simple coding schemes that achieve a sum-rate upper bound to within a constant number of bits for any SNR. Finally, the gDoF of the channel is compared to that of the non-cooperative interference channel and to that of the non-causal cognitive channel to identify the parameter regimes where half-duplex causal cognition is useless in practice or attains its ideal ultimate limit, respectively.

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arXiv2013

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 non-causal knowledge of the other source's message. First the sum-capacity of the symmetric GCCIC is determined to within a constant gap. Then, the insights gained from the derivation of the symmetric sum-capacity are extended to characterize the whole capacity region to within a constant gap for more general cases. In particular, the capacity is determined (a) to within 2 bits for the fully connected GCCIC when, roughly speaking, the interference is not weak at both receivers, (b) to within 2 bits for the Z-channel, i.e., when there is no interference from the primary user, and (c) to within 2 bits for the S-channel, i.e., when there is no interference from the secondary user. 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 lights into the parameter regimes and network topologies that in practice might provide an unbounded throughput gain compared to currently available (non cognitive) technologies.

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arXiv2013

Gaussian Half-Duplex Relay Networks: improved constant gap and connections with the assignment problem

This paper considers a general Gaussian relay network where a source transmits a message to a destination with the help of N half-duplex relays. It proves that the information theoretic cut-set upper bound to the capacity can be achieved to within 2:021(N +2) bits with noisy network coding, thereby reducing the previously known gap. Further improved gap results are presented for more structured networks like diamond networks. It is then shown that the generalized Degrees-of-Freedom of a general Gaussian half-duplex relay 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, known in graph theory as the assignment problem, for which efficient numerical algorithms exist. The optimal schedule, that is, the optimal value of the 2^N possible transmit-receive configurations/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 2 relays, that only 3 out of the 4 possible states have strictly positive probability. Extensive experimental results show that, for a general N-relay network with N<9, the optimal schedule has at most N +1 states with strictly positive probability. As an extension of a conjecture presented for diamond networks, it is conjectured that this result holds for any HD relay network and any number of relays. Finally, a 2-relay network is studied to determine 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.

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arXiv2013

On Gaussian Half-Duplex Relay Networks

This paper considers Gaussian relay networks where a source transmits a message to a sink terminal with the help of one or more relay nodes. The relays work in half-duplex mode, in the sense that they can not transmit and receive at the same time. For the case of one relay, the generalized Degrees-of-Freedom is characterized first and then it is shown that capacity can be achieved to within a constant gap regardless of the actual value of the channel parameters. Different achievable schemes are presented with either deterministic or random switch for the relay node. It is shown that random switch in general achieves higher rates than deterministic switch. For the case of K relays, it is shown that the generalized Degrees-of-Freedom can be obtained by solving a linear program and that capacity can be achieved to within a constant gap of K/2log(4K). This gap may be further decreased by considering more structured networks such as, for example, the diamond network.

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