arXiv subjects

Muriel Medard

Publications and source records attributed to Muriel Medard.

At least 91 records · Page 5Linked to original sources

arXiv2012

Toward Sustainable Networking: Storage Area Networks with Network Coding

This manuscript provides a model to characterize the energy savings of network coded storage (NCS) in storage area networks (SANs). We consider blocking probability of drives as our measure of performance. A mapping technique to analyze SANs as independent M/G/K/K queues is presented, and blocking probabilities for uncoded storage schemes and NCS are derived and compared. We show that coding operates differently than the amalgamation of file chunks and energy savings are shown to scale well with striping number. We illustrate that for enterprise-level SANs energy savings of 20-50% can be realized.

cs.DC↗

arXiv2012

Systematic Network Coding with the Aid of a Full-Duplex Relay

A characterization of systematic network coding over multi-hop wireless networks is key towards understanding the trade-off between complexity and delay performance of networks that preserve the systematic structure. This paper studies the case of a relay channel, where the source's objective is to deliver a given number of data packets to a receiver with the aid of a relay. The source broadcasts to both the receiver and the relay using one frequency, while the relay uses another frequency for transmissions to the receiver, allowing for a full-duplex operation of the relay. We analyze the decoding complexity and delay performance of two types of relays: one that preserves the systematic structure of the code from the source; another that does not. A systematic relay forwards uncoded packets upon reception, but transmits coded packets to the receiver after receiving the first coded packet from the source. On the other hand, a non-systematic relay always transmits linear combinations of previously received packets. We compare the performance of these two alternatives by analytically characterizing the expected transmission completion time as well as the number of uncoded packets forwarded by the relay. Our numerical results show that, for a poor channel between the source and the receiver, preserving the systematic structure at the relay (i) allows a significant increase in the number of uncoded packets received by the receiver, thus reducing the decoding complexity, and (ii) preserves close to optimal delay performance.

cs.NI↗

arXiv2012

QoE-aware Media Streaming in Technology and Cost Heterogeneous Networks

We present a framework for studying the problem of media streaming in technology and cost heterogeneous environments. We first address the problem of efficient streaming in a technology-heterogeneous setting. We employ random linear network coding to simplify the packet selection strategies and alleviate issues such as duplicate packet reception. Then, we study the problem of media streaming from multiple cost-heterogeneous access networks. Our objective is to characterize analytically the trade-off between access cost and user experience. We model the Quality of user Experience (QoE) as the probability of interruption in playback as well as the initial waiting time. We design and characterize various control policies, and formulate the optimal control problem using a Markov Decision Process (MDP) with a probabilistic constraint. We present a characterization of the optimal policy using the Hamilton-Jacobi-Bellman (HJB) equation. For a fluid approximation model, we provide an exact and explicit characterization of a threshold policy and prove its optimality using the HJB equation. Our simulation results show that under properly designed control policy, the existence of alternative access technology as a complement for a primary access network can significantly improve the user experience without any bandwidth over-provisioning.

eess.SY↗

arXiv2012

Computing Bounds on Network Capacity Regions as a Polytope Reconstruction Problem

We define a notion of network capacity region of networks that generalizes the notion of network capacity defined by Cannons et al. and prove its notable properties such as closedness, boundedness and convexity when the finite field is fixed. We show that the network routing capacity region is a computable rational polytope and provide exact algorithms and approximation heuristics for computing the region. We define the semi-network linear coding capacity region, with respect to a fixed finite field, that inner bounds the corresponding network linear coding capacity region, show that it is a computable rational polytope, and provide exact algorithms and approximation heuristics. We show connections between computing these regions and a polytope reconstruction problem and some combinatorial optimization problems, such as the minimum cost directed Steiner tree problem. We provide an example to illustrate our results. The algorithms are not necessarily polynomial-time.

cs.IT↗

arXiv2012

Joint Coding and Scheduling Optimization in Wireless Systems with Varying Delay Sensitivities

Throughput and per-packet delay can present strong trade-offs that are important in the cases of delay sensitive applications.We investigate such trade-offs using a random linear network coding scheme for one or more receivers in single hop wireless packet erasure broadcast channels. We capture the delay sensitivities across different types of network applications using a class of delay metrics based on the norms of packet arrival times. With these delay metrics, we establish a unified framework to characterize the rate and delay requirements of applications and optimize system parameters. In the single receiver case, we demonstrate the trade-off between average packet delay, which we view as the inverse of throughput, and maximum ordered inter-arrival delay for various system parameters. For a single broadcast channel with multiple receivers having different delay constraints and feedback delays, we jointly optimize the coding parameters and time-division scheduling parameters at the transmitters. We formulate the optimization problem as a Generalized Geometric Program (GGP). This approach allows the transmitters to adjust adaptively the coding and scheduling parameters for efficient allocation of network resources under varying delay constraints. In the case where the receivers are served by multiple non-interfering wireless broadcast channels, the same optimization problem is formulated as a Signomial Program, which is NP-hard in general. We provide approximation methods using successive formulation of geometric programs and show the convergence of approximations.

cs.NI↗

arXiv2011

Time-Stampless Adaptive Nonuniform Sampling for Stochastic Signals

In this paper, we introduce a time-stampless adaptive nonuniform sampling (TANS) framework, in which time increments between samples are determined by a function of the $m$ most recent increments and sample values. Since only past samples are used in computing time increments, it is not necessary to save sampling times (time stamps) for use in the reconstruction process. We focus on two TANS schemes for discrete-time stochastic signals: a greedy method, and a method based on dynamic programming. We analyze the performances of these schemes by computing (or bounding) their trade-offs between sampling rate and expected reconstruction distortion for autoregressive and Markovian signals. Simulation results support the analysis of the sampling schemes. We show that, by opportunistically adapting to local signal characteristics, TANS may lead to improved power efficiency in some applications.

cs.IT↗

arXiv2011

A Power Efficient Sensing/Communication Scheme: Joint Source-Channel-Network Coding by Using Compressive Sensing

We propose a joint source-channel-network coding scheme, based on compressive sensing principles, for wireless networks with AWGN channels (that may include multiple access and broadcast), with sources exhibiting temporal and spatial dependencies. Our goal is to provide a reconstruction of sources within an allowed distortion level at each receiver. We perform joint source-channel coding at each source by randomly projecting source values to a lower dimensional space. We consider sources that satisfy the restricted eigenvalue (RE) condition as well as more general sources for which the randomness of the network allows a mapping to lower dimensional spaces. Our approach relies on using analog random linear network coding. The receiver uses compressive sensing decoders to reconstruct sources. Our key insight is the fact that, compressive sensing and analog network coding both preserve the source characteristics required for compressive sensing decoding.

cs.IT↗

arXiv2011

Deterministic Network Model Revisited: An Algebraic Network Coding Approach

The capacity of multiuser networks has been a long-standing problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate multiuser wireless networks. This model, known as the ADT network model, takes into account the broadcast nature of wireless medium and interference. We show that the ADT network model can be described within the algebraic network coding framework introduced by Koetter and Medard. We prove that the ADT network problem can be captured by a single matrix, and show that the min-cut of an ADT network is the rank of this matrix; thus, eliminating the need to optimize over exponential number of cuts between two nodes to compute the min-cut of an ADT network. We extend the capacity characterization for ADT networks to a more general set of connections, including single unicast/multicast connection and non-multicast connections such as multiple multicast, disjoint multicast, and two-level multicast. We also provide sufficiency conditions for achievability in ADT networks for any general connection set. In addition, we show that random linear network coding, a randomized distributed algorithm for network code construction, achieves the capacity for the connections listed above. Furthermore, we extend the ADT networks to those with random erasures and cycles (thus, allowing bi-directional links). In addition, we propose an efficient linear code construction for the deterministic wireless multicast relay network model. Avestimehr et al.'s proposed code construction is not guaranteed to be efficient and may potentially involve an infinite block length. Unlike several previous coding schemes, we do not attempt to find flows in the network. Instead, for a layered network, we maintain an invariant where it is required that at each stage of the code construction, certain sets of codewords are linearly independent.

cs.IT↗

arXiv2011

Completion Time Minimization and Robust Power Control in Wireless Packet Networks

A wireless packet network is considered in which each user transmits a stream of packets to its destination. The transmit power of each user interferes with the transmission of all other users. A convex cost function of the completion times of the user packets is minimized by optimally allocating the users' transmission power subject to their respective power constraints. At all ranges of SINR, completion time minimization can be formulated as a convex optimization problem and hence can be efficiently solved. In particular, although the feasible rate region of the wireless network is non-convex, its corresponding completion time region is shown to be convex. When channel knowledge is imperfect, robust power control is considered based on the channel fading distribution subject to outage probability constraints. The problem is shown to be convex when the fading distribution is log-concave in exponentiated channel power gains; e.g., when each user is under independent Rayleigh, Nakagami, or log-normal fading. Applying the optimization frameworks in a wireless cellular network, the average completion time is significantly reduced as compared to full power transmission.

cs.IT↗

arXiv2011

Localized Dimension Growth in Random Network Coding: A Convolutional Approach

We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The lengths of local encoding kernels increase with time until the global encoding kernel matrices at related sink nodes all have full rank. Instead of estimating the necessary field size a priori, ARCNC operates in a small finite field. It 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 with ARCNC. We show through analysis that this method performs no worse than random linear network codes in general networks, and can provide significant gains in terms of average decoding delay in combination networks.

cs.IT↗

arXiv2011

On the Order Optimality of Large-scale Underwater Networks

Capacity scaling laws are analyzed in an underwater acoustic network with $n$ regularly located nodes on a square, in which both bandwidth and received signal power can be limited significantly. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of $n$. In the network, we characterize an attenuation parameter that depends on the frequency scaling as well as the transmission distance. Cut-set upper bounds on the throughput scaling are then derived in both extended and dense networks having unit node density and unit area, respectively. It is first analyzed that under extended networks, the upper bound is inversely proportional to the attenuation parameter, thus resulting in a highly power-limited network. Interestingly, it is seen that the upper bound for extended networks is intrinsically related to the attenuation parameter but not the spreading factor. On the other hand, in dense networks, we show that there exists either a bandwidth or power limitation, or both, according to the path-loss attenuation regimes, thus yielding the upper bound that has three fundamentally different operating regimes. Furthermore, we describe an achievable scheme based on the simple nearest-neighbor multi-hop (MH) transmission. We show that under extended networks, the MH scheme is order-optimal for all the operating regimes. An achievability result is also presented in dense networks, where the operating regimes that guarantee the order optimality are identified. It thus turns out that frequency scaling is instrumental towards achieving the order optimality in the regimes. Finally, these scaling results are extended to a random network realization. As a result, vital information for fundamental limits of a variety of underwater network scenarios is provided by showing capacity scaling laws.

cs.IT↗

arXiv2011

When Both Transmitting and Receiving Energies Matter: An Application of Network Coding in Wireless Body Area Networks

A network coding scheme for practical implementations of wireless body area networks is presented, with the objective of providing reliability under low-energy constraints. We propose a simple network layer protocol for star networks, adapting redundancy based on both transmission and reception energies for data and control packets, as well as channel conditions. Our numerical results show that even for small networks, the amount of energy reduction achievable can range from 29% to 87%, as the receiving energy per control packet increases from equal to much larger than the transmitting energy per data packet. The achievable gains increase as a) more nodes are added to the network, and/or b) the channels seen by different sensor nodes become more asymmetric.

cs.NI↗

arXiv2010

Compressive Sensing Over Networks

In this paper, we demonstrate some applications of compressive sensing over networks. We make a connection between compressive sensing and traditional information theoretic techniques in source coding and channel coding. Our results provide an explicit trade-off between the rate and the decoding complexity. The key difference of compressive sensing and traditional information theoretic approaches is at their decoding side. Although optimal decoders to recover the original signal, compressed by source coding have high complexity, the compressive sensing decoder is a linear or convex optimization. First, we investigate applications of compressive sensing on distributed compression of correlated sources. Here, by using compressive sensing, we propose a compression scheme for a family of correlated sources with a modularized decoder, providing a trade-off between the compression rate and the decoding complexity. We call this scheme Sparse Distributed Compression. We use this compression scheme for a general multicast network with correlated sources. Here, we first decode some of the sources by a network decoding technique and then, we use a compressive sensing decoder to obtain the whole sources. Then, we investigate applications of compressive sensing on channel coding. We propose a coding scheme that combines compressive sensing and random channel coding for a high-SNR point-to-point Gaussian channel. We call this scheme Sparse Channel Coding. We propose a modularized decoder providing a trade-off between the capacity loss and the decoding complexity. At the receiver side, first, we use a compressive sensing decoder on a noisy signal to obtain a noisy estimate of the original signal and then, we apply a traditional channel coding decoder to find the original signal.

cs.IT↗

arXiv2010

On Network Functional Compression

In this paper, we consider different aspects of the network functional compression problem where computation of a function (or, some functions) of sources located at certain nodes in a network is desired at receiver(s). The rate region of this problem has been considered in the literature under certain restrictive assumptions, particularly in terms of the network topology, the functions and the characteristics of the sources. In this paper, we present results that significantly relax these assumptions. Firstly, we consider this problem for an arbitrary tree network and asymptotically lossless computation. We show that, for depth one trees with correlated sources, or for general trees with independent sources, a modularized coding scheme based on graph colorings and Slepian-Wolf compression performs arbitrarily closely to rate lower bounds. For a general tree network with independent sources, optimal computation to be performed at intermediate nodes is derived. We introduce a necessary and sufficient condition on graph colorings of any achievable coding scheme, called coloring connectivity condition (C.C.C.). Secondly, we investigate the effect of having several functions at the receiver. In this problem, we derive a rate region and propose a coding scheme based on graph colorings. Thirdly, we consider the functional compression problem with feedback. We show that, in this problem, unlike Slepian-Wolf compression, by having feedback, one may outperform rate bounds of the case without feedback. Fourthly, we investigate functional computation problem with distortion. We compute a rate-distortion region for this problem. Then, we propose a simple suboptimal coding scheme with a non-trivial performance guarantee. Finally, we introduce cases where finding minimum entropy colorings and therefore, optimal coding schemes can be performed in polynomial time.

cs.IT↗

arXiv2010

Algebraic Watchdog: Mitigating Misbehavior in Wireless Network Coding

We propose a secure scheme for wireless network coding, called the algebraic watchdog. By enabling nodes to detect malicious behaviors probabilistically and use overheard messages to police their downstream neighbors locally, the algebraic watchdog delivers a secure global self-checking network. Unlike traditional Byzantine detection protocols which are receiver-based, this protocol gives the senders an active role in checking the node downstream. The key idea is inspired by Marti et al.'s watchdog-pathrater, which attempts to detect and mitigate the effects of routing misbehavior. As an initial building block of a such system, we first focus on a two-hop network. We present a graphical model to understand the inference process nodes execute to police their downstream neighbors; as well as to compute, analyze, and approximate the probabilities of misdetection and false detection. In addition, we present an algebraic analysis of the performance using an hypothesis testing framework that provides exact formulae for probabilities of false detection and misdetection. We then extend the algebraic watchdog to a more general network setting, and propose a protocol in which we can establish trust in coded systems in a distributed manner. We develop a graphical model to detect the presence of an adversarial node downstream within a general multi-hop network. The structure of the graphical model (a trellis) lends itself to well-known algorithms, such as the Viterbi algorithm, which can compute the probabilities of misdetection and false detection. We show analytically that as long as the min-cut is not dominated by the Byzantine adversaries, upstream nodes can monitor downstream neighbors and allow reliable communication with certain probability. Finally, we present simulation results that support our analysis.

cs.CR↗

arXiv2010

Minimum cost mirror sites using network coding: Replication vs. coding at the source nodes

Content distribution over networks is often achieved by using mirror sites that hold copies of files or portions thereof to avoid congestion and delay issues arising from excessive demands to a single location. Accordingly, there are distributed storage solutions that divide the file into pieces and place copies of the pieces (replication) or coded versions of the pieces (coding) at multiple source nodes. We consider a network which uses network coding for multicasting the file. There is a set of source nodes that contains either subsets or coded versions of the pieces of the file. The cost of a given storage solution is defined as the sum of the storage cost and the cost of the flows required to support the multicast. Our interest is in finding the storage capacities and flows at minimum combined cost. We formulate the corresponding optimization problems by using the theory of information measures. In particular, we show that when there are two source nodes, there is no loss in considering subset sources. For three source nodes, we derive a tight upper bound on the cost gap between the coded and uncoded cases. We also present algorithms for determining the content of the source nodes.

cs.IT↗

arXiv2010

A Theory of Network Equivalence, Parts I and II

A family of equivalence tools for bounding network capacities is introduced. Part I treats networks of point-to-point channels. The main result is roughly as follows. Given a network of noisy, independent, memoryless point-to-point channels, a collection of communication demands can be met on the given network if and only if it can be met on another network where each noisy channel is replaced by a noiseless bit pipe with throughput equal to the noisy channel capacity. This result was known previously for the case of a single-source multicast demand. The result given here treats general demands -- including, for example, multiple unicast demands -- and applies even when the achievable rate region for the corresponding demands is unknown in the noiseless network. In part II, definitions of upper and lower bounding channel models for general channels are introduced. By these definitions, a collection of communication demands can be met on a network of independent channels if it can be met on a network where each channel is replaced by its lower bounding model andonly if it can be met on a network where each channel is replaced by its upper bounding model. This work derives general conditions under which a network of noiseless bit pipes is an upper or lower bounding model for a multiterminal channel. Example upper and lower bounding models for broadcast, multiple access, and interference channels are given. It is then shown that bounding the difference between the upper and lower bounding models for a given channel yields bounds on the accuracy of network capacity bounds derived using those models. By bounding the capacity of a network of independent noisy channels by the network coding capacity of a network of noiseless bit pipes, this approach represents one step towards the goal of building computational tools for bounding network capacities.

cs.IT↗

arXiv2010

Modeling Network Coded TCP Throughput: A Simple Model and its Validation

We analyze the performance of TCP and TCP with network coding (TCP/NC) in lossy wireless networks. We build upon the simple framework introduced by Padhye et al. and characterize the throughput behavior of classical TCP as well as TCP/NC as a function of erasure rate, round-trip time, maximum window size, and duration of the connection. Our analytical results show that network coding masks erasures and losses from TCP, thus preventing TCP's performance degradation in lossy networks, such as wireless networks. It is further seen that TCP/NC has significant throughput gains over TCP. In addition, we simulate TCP and TCP/NC to verify our analysis of the average throughput and the window evolution. Our analysis and simulation results show very close concordance and support that TCP/NC is robust against erasures. TCP/NC is not only able to increase its window size faster but also to maintain a large window size despite losses within the network, whereas TCP experiences window closing essentially because losses are mistakenly attributed to congestion.

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