arXiv subjects

Muriel Médard

Publications and source records attributed to Muriel Médard.

At least 127 records · Page 7Linked to original sources

arXiv2014

On Scalability of Wireless Networks: A Practical Primer for Large Scale Cooperation

An intuitive overview of the scalability of a variety of types of wireless networks is presented. Simple heuris- tic arguments are demonstrated here for scaling laws presented in other works, as well as for conditions not previously considered in the literature. Unicast and multicast messages, topology, hierarchy, and effects of reliability protocols are discussed. We show how two key factors, bottlenecks and erasures, can often domi- nate the network scaling behavior. Scaling of through- put or delay with the number of transmitting nodes, the number of receiving nodes, and the file size is described.

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arXiv2013

Bounds on inference

Lower bounds for the average probability of error of estimating a hidden variable X given an observation of a correlated random variable Y, and Fano's inequality in particular, play a central role in information theory. In this paper, we present a lower bound for the average estimation error based on the marginal distribution of X and the principal inertias of the joint distribution matrix of X and Y. Furthermore, we discuss an information measure based on the sum of the largest principal inertias, called k-correlation, which generalizes maximal correlation. We show that k-correlation satisfies the Data Processing Inequality and is convex in the conditional distribution of Y given X. Finally, we investigate how to answer a fundamental question in inference and privacy: given an observation Y, can we estimate a function f(X) of the hidden random variable X with an average error below a certain threshold? We provide a general method for answering this question using an approach based on rate-distortion theory.

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arXiv2013

Resolution-aware network coded storage

In this paper, we show that coding can be used in storage area networks (SANs) to improve various quality of service metrics under normal SAN operating conditions, without requiring additional storage space. For our analysis, we develop a model which captures modern characteristics such as constrained I/O access bandwidth limitations. Using this model, we consider two important cases: single-resolution (SR) and multi-resolution (MR) systems. For SR systems, we use blocking probability as the quality of service metric and propose the network coded storage (NCS) scheme as a way to reduce blocking probability. The NCS scheme codes across file chunks in time, exploiting file striping and file duplication. Under our assumptions, we illustrate cases where SR NCS provides an order of magnitude savings in blocking probability. For MR systems, we introduce saturation probability as a quality of service metric to manage multiple user types, and we propose the uncoded resolution- aware storage (URS) and coded resolution-aware storage (CRS) schemes as ways to reduce saturation probability. In MR URS, we align our MR layout strategy with traffic requirements. In MR CRS, we code videos across MR layers. Under our assumptions, we illustrate that URS can in some cases provide an order of magnitude gain in saturation probability over classic non-resolution aware systems. Further, we illustrate that CRS provides additional saturation probability savings over URS.

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arXiv2013

A Novel Network Coded Parallel Transmission Framework for High-Speed Ethernet

Parallel transmission, as defined in high-speed Ethernet standards, enables to use less expensive optoelectronics and offers backwards compatibility with legacy Optical Transport Network (OTN) infrastructure. However, optimal parallel transmission does not scale to large networks, as it requires computationally expensive multipath routing algorithms to minimize differential delay, and thus the required buffer size, optimize traffic splitting ratio, and ensure frame synchronization. In this paper, we propose a novel framework for high-speed Ethernet, which we refer to as network coded parallel transmission, capable of effective buffer management and frame synchronization without the need for complex multipath algorithms in the OTN layer. We show that using network coding can reduce the delay caused by packet reordering at the receiver, thus requiring a smaller overall buffer size, while improving the network throughput. We design the framework in full compliance with high-speed Ethernet standards specified in IEEE802.3ba and present solutions for network encoding, data structure of coded parallel transmission, buffer management and decoding at the receiver side. The proposed network coded parallel transmission framework is simple to implement and represents a potential major breakthrough in the system design of future high-speed Ethernet.

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arXiv2013

Localized Dimension Growth: A Convolutional Random Network Coding Approach to Managing Memory and Decoding Delay

We consider an \textit{Adaptive Random Convolutional Network Coding} (ARCNC) algorithm to address the issue of field size in random network coding for multicast, and study its memory and decoding delay performances through both analysis and numerical simulations. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The cardinality of local encoding kernels increases with time until the global encoding kernel matrices at related sink nodes have full rank.ARCNC adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code. Because convolutional codes of different constraint lengths can coexist in different portions of the network, reductions in decoding delay and memory overheads can be achieved. We show that this method performs no worse than random linear network codes in terms of decodability, and can provide significant gains in terms of average decoding delay or memory in combination, shuttle and random geometric networks.

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arXiv2012

Lists that are smaller than their parts: A coding approach to tunable secrecy

We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show that such codes can be analyzed in the context of a novel information-theoretic metric, ε-symbol secrecy, that encompasses both the one-time pad and traditional rate-based asymptotic metrics, but, like most cryptographic constructs, can be applied in non-asymptotic settings. We derive fundamental bounds for ε-symbol secrecy and demonstrate how these bounds can be achieved with MDS codes when the source is uniformly distributed. We discuss applications and implementation issues of our codes.

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arXiv2012

Bounded-Contention Coding for Wireless Networks in the High SNR Regime

Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain faster algorithms for communication in such networks. This paper proposes a novel approach for wireless communication, which embraces collisions rather than avoiding them, over an additive channel. It introduces a coding technique called Bounded-Contention Coding (BCC) that allows collisions to be successfully decoded by the receiving nodes into the original transmissions and whose complexity depends on a bound on the contention among the transmitters. BCC enables deterministic local broadcast in a network with n nodes and at most a transmitters with information of l bits each within O(a log n + al) bits of communication with full-duplex radios, and O((a log n + al)(log n)) bits, with high probability, with half-duplex radios. When combined with random linear network coding, BCC gives global broadcast within O((D + a + log n)(a log n + l)) bits, with high probability. This also holds in dynamic networks that can change arbitrarily over time by a worst-case adversary. When no bound on the contention is given, it is shown how to probabilistically estimate it and obtain global broadcast that is adaptive to the true contention in the network.

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arXiv2012

Network Coded Gossip with Correlated Data

We design and analyze gossip algorithms for networks with correlated data. In these networks, either the data to be distributed, the data already available at the nodes, or both, are correlated. This model is applicable for a variety of modern networks, such as sensor, peer-to-peer and content distribution networks. Although coding schemes for correlated data have been studied extensively, the focus has been on characterizing the rate region in static memory-free networks. In a gossip-based scheme, however, nodes communicate among each other by continuously exchanging packets according to some underlying communication model. The main figure of merit in this setting is the stopping time -- the time required until nodes can successfully decode. While Gossip schemes are practical, distributed and scalable, they have only been studied for uncorrelated data. We wish to close this gap by providing techniques to analyze network coded gossip in (dynamic) networks with correlated data. We give a clean framework for oblivious network models that applies to a multitude of network and communication scenarios, specify a general setting for distributed correlated data, and give tight bounds on the stopping times of network coded protocols in this wide range of scenarios.

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arXiv2012

Reducibility of joint relay positioning and flow optimization problem

This paper shows how to reduce the otherwise hard joint relay positioning and flow optimization problem into a sequence a two simpler decoupled problems. We consider a class of wireless multicast hypergraphs mainly characterized by their hyperarc rate functions, that are increasing and convex in power, and decreasing in distance between the transmit node and the farthest end node of the hyperarc. The set-up consists of a single multicast flow session involving a source, multiple destinations and a relay that can be positioned freely. The first problem formulates the relay positioning problem in a purely geometric sense, and once the optimal relay position is obtained the second problem addresses the flow optimization. Furthermore, we present simple and efficient algorithms to solve these problems.

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arXiv2011

Speeding Multicast by Acknowledgment Reduction Technique (SMART)

We present a novel feedback protocol for wireless broadcast networks that utilize linear network coding. We consider transmission of packets from one source to many receivers over a single-hop broadcast erasure channel. Our method utilizes a predictive model to request feedback only when the probability that all receivers have completed decoding is significant. In addition, our proposed NACK-based feedback mechanism enables all receivers to request, within a single time slot, the number of retransmissions needed for successful decoding. We present simulation results as well as analytical results that show the favorable scalability of our technique as the number of receivers, file size, and packet erasure probability increase. We also show the robustness of this scheme to uncertainty in the predictive model, including uncertainty in the number of receiving nodes and the packet erasure probability, as well as to losses of the feedback itself. Our scheme, SMART, is shown to perform nearly as well as an omniscient transmitter that requires no feedback. Furthermore, SMART, is shown to outperform current state of the art methods at any given erasure probability, file size, and numbers of receivers.

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arXiv2011

Effects of MAC Approaches on Non-Monotonic Saturation with COPE - A Simple Case Study

We construct a simple network model to provide insight into network design strategies. We show that the model can be used to address various approaches to network coding, MAC, and multi-packet reception so that their effects on network throughput can be evaluated. We consider several topology components which exhibit the same non-monotonic saturation behavior found within the Katti et. al. COPE experiments. We further show that fairness allocation by the MAC can seriously impact performance and cause this non-monotonic saturation. Using our model, we develop a MAC that provides monotonic saturation, higher saturation throughput gains and fairness among flows rather than nodes. The proposed model provides an estimate of the achievable gains for the cross-layer design of network coding, multi-packet reception, and MAC showing that super-additive throughput gains on the order of six times that of routing are possible.

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arXiv2011

Going Beyond Pollution Attacks: Forcing Byzantine Clients to Code Correctly

Network coding achieves optimal throughput in multicast networks. However, throughput optimality \emph{relies} on the network nodes or routers to code \emph{correctly}. A Byzantine node may introduce junk packets in the network (thus polluting downstream packets and causing the sinks to receive the wrong data) or may choose coding coefficients in a way that significantly reduces the throughput of the network. Most prior work focused on the problem of Byzantine nodes polluting packets. However, even if a Byzantine node does not pollute packets, he can still affect significantly the throughput of the network by not coding correctly. No previous work attempted to verify if a certain node \emph{coded correctly using random coefficients} over \emph{all} of the packets he was supposed to code over. We provide two novel protocols (which we call PIP and Log-PIP) for detecting whether a node coded correctly over all the packets received (i.e., according to a random linear network coding algorithm). Our protocols enable any node in the network to examine a packet received from another node by running a "verification test". With our protocols, the worst an adversary can do and still pass the packet verification test is in fact equivalent to random linear network coding, which has been shown to be optimal in multicast networks. Our protocols resist collusion among nodes and are applicable to a variety of settings. Our topology simulations show that the throughput in the worst case for our protocol is two to three times larger than the throughput in various adversarial strategies allowed by prior work. We implemented our protocols in C/C++ and Java, as well as incorporated them on the Android platform (Nexus One). Our evaluation shows that our protocols impose modest overhead.

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arXiv2011

MAC Centered Cooperation - Synergistic Design of Network Coding, Multi-Packet Reception, and Improved Fairness to Increase Network Throughput

We design a cross-layer approach to aid in develop- ing a cooperative solution using multi-packet reception (MPR), network coding (NC), and medium access (MAC). We construct a model for the behavior of the IEEE 802.11 MAC protocol and apply it to key small canonical topology components and their larger counterparts. The results obtained from this model match the available experimental results with fidelity. Using this model, we show that fairness allocation by the IEEE 802.11 MAC can significantly impede performance; hence, we devise a new MAC that not only substantially improves throughput, but provides fairness to flows of information rather than to nodes. We show that cooperation between NC, MPR, and our new MAC achieves super-additive gains of up to 6.3 times that of routing with the standard IEEE 802.11 MAC. Furthermore, we extend the model to analyze our MAC's asymptotic and throughput behaviors as the number of nodes increases or the MPR capability is limited to only a single node. Finally, we show that although network performance is reduced under substantial asymmetry or limited implementation of MPR to a central node, there are some important practical cases, even under these conditions, where MPR, NC, and their combination provide significant gains.

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arXiv2011

On the geometry of wireless network multicast in 2-D

We provide a geometric solution to the problem of optimal relay positioning to maximize the multicast rate for low-SNR networks. The networks we consider, consist of a single source, multiple receivers and the only intermediate and locatable node as the relay. We construct network the hypergraph of the system nodes from the underlying information theoretic model of low-SNR regime that operates using superposition coding and FDMA in conjunction (which we call the "achievable hypergraph model"). We make the following contributions. 1) We show that the problem of optimal relay positioning maximizing the multicast rate can be completely decoupled from the flow optimization by noticing and exploiting geometric properties of multicast flow. 2) All the flow maximizing the multicast rate is sent over at most two paths, in succession. The relay position is dependent only on one path (out of the two), irrespective of the number of receiver nodes in the system. Subsequently, we propose simple and efficient geometric algorithms to compute the optimal relay position. 3) Finally, we show that in our model at the optimal relay position, the difference between the maximized multicast rate and the cut-set bound is minimum. We solve the problem for all (Ps,Pr) pairs of source and relay transmit powers and the path loss exponent αgreater than 2.

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arXiv2011

Optimality of Network Coding in Packet Networks

We resolve the question of optimality for a well-studied packetized implementation of random linear network coding, called PNC. In PNC, in contrast to the classical memoryless setting, nodes store received information in memory to later produce coded packets that reflect this information. PNC is known to achieve order optimal stopping times for the many-to-all multicast problem in many settings. We give a reduction that captures exactly how PNC and other network coding protocols use the memory of the nodes. More precisely, we show that any such protocol implementation induces a transformation which maps an execution of the protocol to an instance of the classical memoryless setting. This allows us to prove that, for any (non-adaptive dynamic) network, PNC converges with high probability in optimal time. In other words, it stops at exactly the first time in which in hindsight it was possible to route information from the sources to each receiver individually. Our technique also applies to variants of PNC, in which each node uses only a finite buffer. We show that, even in this setting, PNC stops exactly within the time in which in hindsight it was possible to route packets given the memory constraint, i.e., that the memory used at each node never exceeds its buffer size. This shows that PNC, even without any feedback or explicit memory management, allows to keep minimal buffer sizes while maintaining its capacity achieving performance.

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arXiv2011

One Packet Suffices - Highly Efficient Packetized Network Coding With Finite Memory

Random Linear Network Coding (RLNC) has emerged as a powerful tool for robust high-throughput multicast. Projection analysis - a recently introduced technique - shows that the distributed packetized RLNC protocol achieves (order) optimal and perfectly pipelined information dissemination in many settings. In the original approach to RNLC intermediate nodes code together all available information. This requires intermediate nodes to keep considerable data available for coding. Moreover, it results in a coding complexity that grows linearly with the size of this data. While this has been identified as a problem, approaches that combine queuing theory and network coding have heretofore not provided a succinct representation of the memory needs of network coding at intermediates nodes. This paper shows the surprising result that, in all settings with a continuous stream of data, network coding continues to perform optimally even if only one packet per node is kept in active memory and used for computations. This leads to an extremely simple RLNC protocol variant with drastically reduced requirements on computational and memory resources. By extending the projection analysis, we show that in all settings in which the RLNC protocol was proven to be optimal its finite memory variant performs equally well. In the same way as the original projection analysis, our technique applies in a wide variety of network models, including highly dynamic topologies that can change completely at any time in an adversarial fashion.

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arXiv2011

Co-Designing Multi-Packet Reception, Network Coding, and MAC Using a Simple Predictive Model

We design a cross-layer approach to optimize the joint use of multi-packet reception and network coding, in order to relieve congestion. We construct a model for the behavior of the 802.11 MAC and apply it to several key canonical topology components and their extensions to any number of nodes. The results obtained from this model match the available experimental results, which are for routing and opportunistic network coding, with fidelity. Using this model, we show that fairness allocation by the MAC can seriously impact performance; hence, we devise a new MAC that not only substantially improves throughput relative to the current 802.11 MAC, but also provides fairness to flows of information rather than to nodes. We show that the proper combination of network coding, multi-packet reception, and our new MAC protocol achieves super-additive throughput gains of up to 6.3 times that of routing alone with the use of the standard 802.11 MAC. Finally, we extend the model to analyze the asymptotic behavior of our new MAC as the number of nodes increases.

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arXiv2011

Optimal relay location and power allocation for low SNR broadcast relay channels

We consider the broadcast relay channel (BRC), where a single source transmits to multiple destinations with the help of a relay, in the limit of a large bandwidth. We address the problem of optimal relay positioning and power allocations at source and relay, to maximize the multicast rate from source to all destinations. To solve such a network planning problem, we develop a three-faceted approach based on an underlying information theoretic model, computational geometric aspects, and network optimization tools. Firstly, assuming superposition coding and frequency division between the source and the relay, the information theoretic framework yields a hypergraph model of the wideband BRC, which captures the dependency of achievable rate-tuples on the network topology. As the relay position varies, so does the set of hyperarcs constituting the hypergraph, rendering the combinatorial nature of optimization problem. We show that the convex hull C of all nodes in the 2-D plane can be divided into disjoint regions corresponding to distinct hyperarcs sets. These sets are obtained by superimposing all k-th order Voronoi tessellation of C. We propose an easy and efficient algorithm to compute all hyperarc sets, and prove they are polynomially bounded. Using the switched hypergraph approach, we model the original problem as a continuous yet non-convex network optimization program. Ultimately, availing on the techniques of geometric programming and $p$-norm surrogate approximation, we derive a good convex approximation. We provide a detailed characterization of the problem for collinearly located destinations, and then give a generalization for arbitrarily located destinations. Finally, we show strong gains for the optimal relay positioning compared to seemingly interesting positions.

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