arXiv subjects

Muriel Médard

Publications and source records attributed to Muriel Médard.

At least 109 records · Page 6Linked to original sources

arXiv2017

Maximum Likelihood Latent Space Embedding of Logistic Random Dot Product Graphs

A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Random Dot Product Graph (RDPG), which can be fit using an efficient spectral method; however, this method is based on a heuristic that can fail, even in simple cases. Here, we consider a closely related latent space model, the Logistic RDPG, which uses a logistic link function to map from latent positions to edge likelihoods. Over this model, we show that asymptotically exact maximum likelihood inference of latent position vectors can be achieved using an efficient spectral method. Our method involves computing top eigenvectors of a normalized adjacency matrix and scaling eigenvectors using a regression step. The novel regression scaling step is an essential part of the proposed method. In simulations, we show that our proposed method is more accurate and more robust than common practices. We also show the effectiveness of our approach over standard real networks of the karate club and political blogs.

stat.ML↗

arXiv2017

The Storage vs Repair Bandwidth Trade-off for Multiple Failures in Clustered Storage Networks

We study the trade-off between storage overhead and inter-cluster repair bandwidth in clustered storage systems, while recovering from multiple node failures within a cluster. A cluster is a collection of $m$ nodes, and there are $n$ clusters. For data collection, we download the entire content from any $k$ clusters. For repair of $t \geq 2$ nodes within a cluster, we take help from $\ell$ local nodes, as well as $d$ helper clusters. We characterize the optimal trade-off under functional repair, and also under exact repair for the minimum storage and minimum inter-cluster bandwidth (MBR) operating points. Our bounds show the following interesting facts: $1)$ When $t|(m-\ell)$ the trade-off is the same as that under $t=1$, and thus there is no advantage in jointly repairing multiple nodes, $2)$ When $t \nmid (m-\ell)$, the optimal file-size at the MBR point under exact repair can be strictly less than that under functional repair. $3)$ Unlike the case of $t=1$, increasing the number of local helper nodes does not necessarily increase the system capacity under functional repair.

cs.IT↗

arXiv2017

Gaussian Intersymbol Interference Channels With Mismatch

This paper considers the problem of channel coding over Gaussian intersymbol interference (ISI) channels with a given metric decoding rule. Specifically, it is assumed that the mismatched decoder has an incorrect assumption on the impulse response function. The mismatch capacity is the highest achievable rate for a given decoding rule. Existing lower bounds to the mismatch capacity for channels and decoding metrics with memory (as in our model) are presented only in the form of multi-letter expressions that have not been calculated in practice. Consequently, they provide little insight on the mismatch problem. In this paper, we derive computable single-letter lower bounds to the mismatch capacity, and discuss some implications of our results. Our achievable rates are based on two ensembles, the ensemble of codewords generated by an autoregressive process, and the ensemble of codewords drawn uniformly over a "type class" of real-valued sequences. Computation of our achievable rates demonstrates non-trivial behavior of the achievable rates as a function of the mismatched parameters. As a simple application of our technique, we derive also the random coding exponent associated with a mismatched decoder which assumes that there is no ISI at all. Finally, we compare our results with universal decoders which are designed outside the true class of channels that we consider in this paper.

cs.IT↗

arXiv2017

Centralized vs Decentralized Multi-Agent Guesswork

We study a notion of guesswork, where multiple agents intend to launch a coordinated brute-force attack to find a single binary secret string, and each agent has access to side information generated through either a BEC or a BSC. The average number of trials required to find the secret string grows exponentially with the length of the string, and the rate of the growth is called the guesswork exponent. We compute the guesswork exponent for several multi-agent attacks. We show that a multi-agent attack reduces the guesswork exponent compared to a single agent, even when the agents do not exchange information to coordinate their attack, and try to individually guess the secret string using a predetermined scheme in a decentralized fashion. Further, we show that the guesswork exponent of two agents who do coordinate their attack is strictly smaller than that of any finite number of agents individually performing decentralized guesswork.

cs.IT↗

arXiv2017

Capacity of Molecular Channels with Imperfect Particle-Intensity Modulation and Detection

This work introduces the particle-intensity channel (PIC) as a model for molecular communication systems and characterizes the properties of the optimal input distribution and the capacity limits for this system. In the PIC, the transmitter encodes information, in symbols of a given duration, based on the number of particles released, and the receiver detects and decodes the message based on the number of particles detected during the symbol interval. In this channel, the transmitter may be unable to control precisely the number of particles released, and the receiver may not detect all the particles that arrive. We demonstrate that the optimal input distribution for this channel always has mass points at zero and the maximum number of particles that can be released. We then consider diffusive particle transport, derive the capacity expression when the input distribution is binary, and show conditions under which the binary input is capacity-achieving. In particular, we demonstrate that when the transmitter cannot generate particles at a high rate, the optimal input distribution is binary.

cs.IT↗

arXiv2017

Principal Inertia Components and Applications

We explore properties and applications of the Principal Inertia Components (PICs) between two discrete random variables $X$ and $Y$. The PICs lie in the intersection of information and estimation theory, and provide a fine-grained decomposition of the dependence between $X$ and $Y$. Moreover, the PICs describe which functions of $X$ can or cannot be reliably inferred (in terms of MMSE) given an observation of $Y$. We demonstrate that the PICs play an important role in information theory, and they can be used to characterize information-theoretic limits of certain estimation problems. In privacy settings, we prove that the PICs are related to fundamental limits of perfect privacy.

cs.IT↗

arXiv2017

Towards Interconnected Virtual Reality: Opportunities, Challenges and Enablers

Just recently, the concept of augmented and virtual reality (AR/VR) over wireless has taken the entire 5G ecosystem by storm spurring an unprecedented interest from both academia, industry and others. Yet, the success of an immersive VR experience hinges on solving a plethora of grand challenges cutting across multiple disciplines. This article underscores the importance of VR technology as a disruptive use case of 5G (and beyond) harnessing the latest development of storage/memory, fog/edge computing, computer vision, artificial intelligence and others. In particular, the main requirements of wireless interconnected VR are described followed by a selection of key enablers, then, research avenues and their underlying grand challenges are presented. Furthermore, we examine three VR case studies and provide numerical results under various storage, computing and network configurations. Finally, this article exposes the limitations of current networks and makes the case for more theory, and innovations to spearhead VR for the masses.

cs.NI↗

arXiv2016

Unified Capacity Limit of Non-coherent Wideband Fading Channels

In non-coherent wideband fading channels where energy rather than spectrum is the limiting resource, peaky and non-peaky signaling schemes have long been considered species apart, as the first approaches asymptotically the capacity of a wideband AWGN channel with the same average SNR, whereas the second reaches a peak rate at some finite critical bandwidth and then falls to zero as bandwidth grows to infinity. In this paper it is shown that this distinction is in fact an artifact of the limited attention paid in the past to the product between the bandwidth and the fraction of time it is in use. This fundamental quantity, called bandwidth occupancy, measures average bandwidth usage over time. For all signaling schemes with the same bandwidth occupancy, achievable rates approach to the wideband AWGN capacity within the same gap as the bandwidth occupancy approaches its critical value, and decrease to zero as the occupancy goes to infinity. This unified analysis produces quantitative closed-form expressions for the ideal bandwidth occupancy, recovers the existing capacity results for (non-)peaky signaling schemes, and unveils a trade-off between the accuracy of approximating capacity with a generalized Taylor polynomial and the accuracy with which the optimal bandwidth occupancy can be bounded.

cs.IT↗

arXiv2016

A Linear Network Code Construction for General Integer Connections Based on the Constraint Satisfaction Problem

The problem of finding network codes for general connections is inherently difficult in capacity constrained networks. Resource minimization for general connections with network coding is further complicated. Existing methods for identifying solutions mainly rely on highly restricted classes of network codes, and are almost all centralized. In this paper, we introduce linear network mixing coefficients for code constructions of general connections that generalize random linear network coding (RLNC) for multicast connections. For such code constructions, we pose the problem of cost minimization for the subgraph involved in the coding solution and relate this minimization to a path-based Constraint Satisfaction Problem (CSP) and an edge-based CSP. While CSPs are NP-complete in general, we present a path-based probabilistic distributed algorithm and an edge-based probabilistic distributed algorithm with almost sure convergence in finite time by applying Communication Free Learning (CFL). Our approach allows fairly general coding across flows, guarantees no greater cost than routing, and shows a possible distributed implementation. Numerical results illustrate the performance improvement of our approach over existing methods.

cs.IT↗

arXiv2016

Maximum Entropy Functions: Approximate Gacs-Korner for Distributed Compression

Consider two correlated sources $X$ and $Y$ generated from a joint distribution $p_{X,Y}$. Their Gács-Körner Common Information, a measure of common information that exploits the combinatorial structure of the distribution $p_{X,Y}$, leads to a source decomposition that exhibits the latent common parts in $X$ and $Y$. Using this source decomposition we construct an efficient distributed compression scheme, which can be efficiently used in the network setting as well. Then, we relax the combinatorial conditions on the source distribution, which results in an efficient scheme with a helper node, which can be thought of as a front-end cache. This relaxation leads to an inherent trade-off between the rate of the helper and the rate reduction at the sources, which we capture by a notion of optimal decomposition. We formulate this as an approximate Gács-Körner optimization. We then discuss properties of this optimization, and provide connections with the maximal correlation coefficient, as well as an efficient algorithm, both through the application of spectral graph theory to the induced bipartite graph of $p_{X,Y}$.

cs.IT↗

arXiv2016

Efficient Coding for Multi-source Networks using Gács-Körner Common Information

Consider a multi-source network coding problem with correlated sources. While the fundamental limits are known, achieving them, in general, involves a computational burden due to the complex decoding process. Efficient solutions, on the other hand, are by large based on source and network coding separation, thus imposing strict topological constraints on the networks which can be solved. In this work, we introduce a novel notion of separation of source and network coding using Gács-Körner Common Information (CI). Unlike existing notions of separation, the sufficient condition for this separation to hold depends on the source structure rather than the network topology. Using the suggested separation scheme, we tackle three important multi-source problems. The first is the multi-source multicast. We construct efficient, zero error source codes, and via properties of the CI completely characterize the resulting rate region. The second is broadcast with side information. We establish a duality between this problem and the classical problem of degraded message set broadcast, and give two code constructions and their associated regions. Finally, we consider the Ahlswede-Korner problem in a network, and give an efficient solution which is tight under the CI constraints.

cs.IT↗

arXiv2015

Can network coding bridge the digital divide in the Pacific?

Conventional TCP performance is significantly impaired under long latency and/or constrained bandwidth. While small Pacific Island states on satellite links experience this in the extreme, small populations and remoteness often rule out submarine fibre connections and their communities struggle to reap the benefits of the Internet. Network-coded TCP (TCP/NC) can increase goodput under high latency and packet loss, but has not been used to tunnel conventional TCP and UDP across satellite links before. We report on a feasibility study aimed at determining expected goodput gain across such TCP/NC tunnels into island targets on geostationary and medium earth orbit satellite links.

cs.IT↗

arXiv2015

Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security

We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless source coding, and another akin to rate-distortion theory. We start by presenting a new information-theoretic metric for security, called symbol secrecy, and derive associated fundamental bounds. We then introduce list-source codes (LSCs), which are a general framework for mapping a key length (entropy) to a list size that an eavesdropper has to resolve in order to recover a secret message. We provide explicit constructions of LSCs, and demonstrate that, when the source is uniformly distributed, the highest level of symbol secrecy for a fixed key length can be achieved through a construction based on minimum-distance separable (MDS) codes. Using an analysis related to rate-distortion theory, we then show how symbol secrecy can be used to determine the probability that an eavesdropper correctly reconstructs functions of the original plaintext. We illustrate how these bounds can be applied to characterize security properties of symmetric-key encryption schemes, and, in particular, extend security claims based on symbol secrecy to a functional setting.

cs.IT↗

arXiv2015

Optimization-Based Linear Network Coding for General Connections of Continuous Flows

For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of network codes in terms of the number of flows allowed to be coded together, and are not entirely distributed. In this paper, we consider a new method for constructing linear network codes for general connections of continuous flows to minimize the total cost of edge use based on mixing. We first formulate the minimumcost network coding design problem. To solve the optimization problem, we propose two equivalent alternative formulations with discrete mixing and continuous mixing, respectively, and develop distributed algorithms to solve them. Our approach allows fairly general coding across flows and guarantees no greater cost than any solution without network coding.

cs.IT↗

arXiv2015

File Updates Under Random/Arbitrary Insertions And Deletions

A client/encoder edits a file, as modeled by an insertion-deletion (InDel) process. An old copy of the file is stored remotely at a data-centre/decoder, and is also available to the client. We consider the problem of throughput- and computationally-efficient communication from the client to the data-centre, to enable the server to update its copy to the newly edited file. We study two models for the source files/edit patterns: the random pre-edit sequence left-to-right random InDel (RPES-LtRRID) process, and the arbitrary pre-edit sequence arbitrary InDel (APES-AID) process. In both models, we consider the regime in which the number of insertions/deletions is a small (but constant) fraction of the original file. For both models we prove information-theoretic lower bounds on the best possible compression rates that enable file updates. Conversely, our compression algorithms use dynamic programming (DP) and entropy coding, and achieve rates that are approximately optimal.

cs.IT↗

arXiv2014

A Coded Shared Atomic Memory Algorithm for Message Passing Architectures

This paper considers the communication and storage costs of emulating atomic (linearizable) multi-writer multi-reader shared memory in distributed message-passing systems. The paper contains three main contributions: (1) We present a atomic shared-memory emulation algorithm that we call Coded Atomic Storage (CAS). This algorithm uses erasure coding methods. In a storage system with $N$ servers that is resilient to $f$ server failures, we show that the communication cost of CAS is $\frac{N}{N-2f}$. The storage cost of CAS is unbounded. (2) We present a modification of the CAS algorithm known as CAS with Garbage Collection (CASGC). The CASGC algorithm is parametrized by an integer $δ$ and has a bounded storage cost. We show that in every execution where the number of write operations that are concurrent with a read operation is no bigger than $δ$, the CASGC algorithm with parameter $δ$ satisfies atomicity and liveness. We explicitly characterize the storage cost of CASGC, and show that it has the same communication cost as CAS. (3) We describe an algorithm known as the Communication Cost Optimal Atomic Storage (CCOAS) algorithm that achieves a smaller communication cost than CAS and CASGC. In particular, CCOAS incurs read and write communication costs of $\frac{N}{N-f}$ measured in terms of number of object values. We also discuss drawbacks of CCOAS as compared with CAS and CASGC.

cs.DC↗

arXiv2014

Quasi-linear Network Coding

We present a heuristic for designing vector non-linear network codes for non-multicast networks, which we call quasi-linear network codes. The method presented has two phases: finding an approximate linear network code over the reals, and then quantizing it to a vector non-linear network code using a fixed-point representation. Apart from describing the method, we draw some links between some network parameters and the rate of the resulting code.

cs.IT↗

arXiv2014

An Exploration of the Role of Principal Inertia Components in Information Theory

The principal inertia components of the joint distribution of two random variables $X$ and $Y$ are inherently connected to how an observation of $Y$ is statistically related to a hidden variable $X$. In this paper, we explore this connection within an information theoretic framework. We show that, under certain symmetry conditions, the principal inertia components play an important role in estimating one-bit functions of $X$, namely $f(X)$, given an observation of $Y$. In particular, the principal inertia components bear an interpretation as filter coefficients in the linear transformation of $p_{f(X)|X}$ into $p_{f(X)|Y}$. This interpretation naturally leads to the conjecture that the mutual information between $f(X)$ and $Y$ is maximized when all the principal inertia components have equal value. We also study the role of the principal inertia components in the Markov chain $B\rightarrow X\rightarrow Y\rightarrow \widehat{B}$, where $B$ and $\widehat{B}$ are binary random variables. We illustrate our results for the setting where $X$ and $Y$ are binary strings and $Y$ is the result of sending $X$ through an additive noise binary channel.

cs.IT↗