arXiv subjects

Christina Fragouli

Publications and source records attributed to Christina Fragouli.

At least 73 records · Page 4Linked to original sources

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

Consistency in the face of change: an adaptive approach to physical layer cooperation

Most existing works on physical-layer (PHY) cooperation (beyond routing) focus on how to best use a given, static relay network--while wireless networks are anything but static. In this paper, we pose a different set of questions: given that we have multiple devices within range, which relay(s) do we use for PHY cooperation, to maintain a consistent target performance? How can we efficiently adapt, as network conditions change? And how important is it, in terms of performance, to adapt? Although adapting to the best path when routing is a well understood problem, how to do so over PHY cooperation networks is an open question. Our contributions are: (1) We demonstrate via theoretical evaluation, a diminishing returns trend as the number of deployed relays increases. (2) Using a simple algorithm based on network metrics, we efficiently select the sub-network to use at any given time to maintain a target reliability. (3) When streaming video from Netflix, we experimentally show (using measurements from a WARP radio testbed employing DIQIF relaying) that our adaptive PHY cooperation scheme provides a throughput gain of 2x over nonadaptive PHY schemes, and a gain of 6x over genie-aided IP-level adaptive routing.

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arXiv2016

A Note on Antenna Selection in Gaussian MIMO Channels: Capacity Guarantees and Bounds

We consider the problem of selecting $k_t \times k_r$ antennas from a Gaussian MIMO channel with $n_t \times n_r$ antennas, where $k_t \leq n_t$ and $k_r \leq n_r$. We prove the following two results that hold universally, in the sense that they do not depend on the channel coefficients: (i) The capacity of the best $k_t \times k_r$ subchannel is always lower bounded by a fraction $\frac{k_t k_r}{n_t n_r}$ of the full capacity (with $n_t \times n_r$ antennas). This bound is tight as the channel coefficients diminish in magnitude. (ii) There always exists a selection of $k_t \times k_r$ antennas (including the best) that achieves a fraction greater than $\frac{\min(k_t ,k_r)}{\min(n_t,n_r)}$ of the full capacity within an additive constant that is independent of the coefficients in the channel matrix. The key mathematical idea that allows us to derive these universal bounds is to directly relate the determinants of principle sub-matrices of a Hermitian matrix to the determinant of the entire matrix.

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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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arXiv2016

Group secret key agreement over state-dependent wireless broadcast channels

We consider a group of $m$ trusted and authenticated nodes that aim to create a shared secret key $K$ over a wireless channel in the presence of an eavesdropper Eve. We assume that there exists a state dependent wireless broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free, noiseless and unlimited rate public channel which is also overheard by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for "linear deterministic" wireless broadcast channels. This model generalizes the packet erasure model studied in literature for wireless broadcast channels. For "state-dependent Gaussian" wireless broadcast channels, we propose an achievability scheme based on a multi-layer wiretap code. Finding the best achievable secret key generation rate leads to solving a non-convex power allocation problem. We show that using a dynamic programming algorithm, one can obtain the best power allocation for this problem. Moreover, we prove the optimality of the proposed achievability scheme for the regime of high-SNR and large-dynamic range over the channel states in the (generalized) degrees of freedom sense.

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arXiv2016

Wireless Network Simplification : Beyond Diamond Networks

We consider an arbitrary layered Gaussian relay network with $L$ layers of $N$ relays each, from which we select subnetworks with $K$ relays per layer. We prove that: (i) For arbitrary $L, N$ and $K = 1$, there always exists a subnetwork that approximately achieves $\frac{2}{(L-1)N + 4}$ $\left(\mbox{resp.}\frac{2}{LN+2}\right)$ of the network capacity for odd $L$ (resp. even $L$), (ii) For $L = 2, N = 3, K = 2$, there always exists a subnetwork that approximately achieves $\frac{1}{2}$ of the network capacity. We also provide example networks where even the best subnetworks achieve exactly these fractions (up to additive gaps). Along the way, we derive some results on MIMO antenna selection and capacity decomposition that may also be of independent interest.

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arXiv2016

A Deterministic Algorithm for Pliable Index Coding

Pliable index coding considers a server with m messages, and n clients where each has as side information a subset of the messages. We seek to minimize the number of transmissions the server should make, so that each client receives (any) one message she does not already have. Previous work has shown that the server can achieve this using O(\log^2(n)) transmissions and needs at least Ω(log(n)) transmissions in the worst case, but finding a code of optimal length is NP-hard. In this paper, we propose a deterministic algorithm that we prove achieves this upper bound, that is, in an order almost as the worst-case optimal code length. We also establish a connection between the pliable index coding problem and the minrank problem over a family of mixed matrices.

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arXiv2015

Content-type coding

This paper is motivated by the observation that, in many cases, we do not need to serve specific messages, but rather, any message within a content-type. Content-type traffic pervades a host of applications today, ranging from search engines and recommender networks to newsfeeds and advertisement networks. The paper asks a novel question: if there are benefits in designing network and channel codes specifically tailored to content-type requests. It provides three examples of content-type formulations to argue that, indeed in some cases we can have significant such benefits.

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arXiv2015

LP formulations for secrecy over erasure networks with feedback

We design polynomial time schemes for secure message transmission over arbitrary networks, in the presence of an eavesdropper, and where each edge corresponds to an erasure channel with public feedback. Our schemes are described through linear programming (LP) formulations, that explicitly select (possibly different) sets of paths for key-generation and message sending. Although our LPs are not always capacity-achieving, they outperform the best known alternatives in the literature, and extend to incorporate several interesting scenaria.

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arXiv2014

Secret Communication over Broadcast Erasure Channels with State-feedback

We consider a 1-to-$K$ communication scenario, where a source transmits private messages to $K$ receivers through a broadcast erasure channel, and the receivers feed back strictly causally and publicly their channel states after each transmission. We explore the achievable rate region when we require that the message to each receiver remains secret - in the information theoretical sense - from all the other receivers. We characterize the capacity of secure communication in all the cases where the capacity of the 1-to-$K$ communication scenario without the requirement of security is known. As a special case, we characterize the secret-message capacity of a single receiver point-to-point erasure channel with public state-feedback in the presence of a passive eavesdropper. We find that in all cases where we have an exact characterization, we can achieve the capacity by using linear complexity two-phase schemes: in the first phase we create appropriate secret keys, and in the second phase we use them to encrypt each message. We find that the amount of key we need is smaller than the size of the message, and equal to the amount of encrypted message the potential eavesdroppers jointly collect. Moreover, we prove that a dishonest receiver that provides deceptive feedback cannot diminish the rate experienced by the honest receivers. We also develop a converse proof which reflects the two-phase structure of our achievability scheme. As a side result, our technique leads to a new outer bound proof for the non-secure communication problem.

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arXiv2014

Secret message capacity of a line network

We investigate the problem of information theoretically secure communication in a line network with erasure channels and state feedback. We consider a spectrum of cases for the private randomness that intermediate nodes can generate, ranging from having intermediate nodes generate unlimited private randomness, to having intermediate nodes generate no private randomness, and all cases in between. We characterize the secret message capacity when either only one of the channels is eavesdropped or all of the channels are eavesdropped, and we develop polynomial time algorithms that achieve these capacities. We also give an outer bound for the case where an arbitrary number of channels is eavesdropped. Our work is the first to characterize the secrecy capacity of a network of arbitrary size, with imperfect channels and feedback. As a side result, we derive the secret key and secret message capacity of an one-hop network, when the source has limited randomness.

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arXiv2014

MicroCast: Cooperative Video Streaming using Cellular and D2D Connections

We consider a group of mobile users, within proximity of each other, who are interested in watching the same online video at roughly the same time. The common practice today is that each user downloads the video independently on her mobile device using her own cellular connection, which wastes access bandwidth and may also lead to poor video quality. We propose a novel cooperative system where each mobile device uses simultaneously two network interfaces: (i) the cellular to connect to the video server and download parts of the video and (ii) WiFi to connect locally to all other devices in the group and exchange those parts. Devices cooperate to efficiently utilize all network resources and are able to adapt to varying wireless network conditions. In the local WiFi network, we exploit overhearing, and we further combine it with network coding. The end result is savings in cellular bandwidth and improved user experience (faster download) by a factor on the order up to the group size. We follow a complete approach, from theory to practice. First, we formulate the problem using a network utility maximization (NUM) framework, decompose the problem, and provide a distributed solution. Then, based on the structure of the NUM solution, we design a modular system called MicroCast and we implement it as an Android application. We provide both simulation results of the NUM solution and experimental evaluation of MicroCast on a testbed consisting of Android phones. We demonstrate that the proposed approach brings significant performance benefits without battery penalty.

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arXiv2013

Cooperative Relaying at Finite SNR -- Role of Quantize-Map-and-Forward

Quantize-Map-and-Forward (QMF) relaying has been shown to achieve the optimal diversity-multiplexing trade-off (DMT) for arbitrary slow fading full-duplex networks as well as for the single-relay half-duplex network. A key reason for this is that quantizing at the noise level suffices to achieve the cut-set bound approximately to within an additive gap, without any requirement of instantaneous channel state information (CSI). However, DMT only captures the high SNR performance and potentially, limited CSI at the relay can improve performance at moderate SNRs. In this work we propose an optimization framework for QMF relaying over slow fading channels. Focusing on vector Gaussian quantizers, we optimize the outage probability for the full-duplex and half-duplex single relay by finding the best quantization level and relay schedule according to the available CSI at the relays. For the N-relay diamond network, we derive an universal quantizer that sharpens the additive approximation gap of QMF from the conventional Θ(N) bits/s/Hz to Θ(log(N)) bits/s/Hz using only network topology information. Analytical solutions to channel-aware optimal quantizers for two-relay and symmetric N-relay diamond networks are also derived. In addition, we prove that suitable hybridizations of our optimized QMF schemes with Decode-Forward (DF) or Dynamic DF protocols provide significant finite SNR gains over the individual schemes.

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arXiv2013

Using Feedback for Secrecy over Graphs

We study the problem of secure message multicasting over graphs in the presence of a passive (node) adversary who tries to eavesdrop in the network. We show that use of feedback, facilitated through the existence of cycles or undirected edges, enables higher rates than possible in directed acyclic graphs of the same mincut. We demonstrate this using code constructions for canonical combination networks (CCNs). We also provide general outer bounds as well as schemes for node adversaries over CCNs.

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arXiv2013

Coding with Encoding Uncertainty

We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding uncertainty as erasures on the edges in the factor graph of the encoder generator matrix. We first take a worst-case approach and find the maximum tolerable number of erasures for perfect error correction. Next, we take a probabilistic approach and derive a sufficient condition on the rate of a set of codes, such that decoding error probability vanishes as blocklength tends to infinity. In both scenarios, due to the inherent asymmetry of the problem, we derive the results from first principles, which indicates that robustness to encoding errors requires new properties of codes different from classical properties.

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