We study set-valued decision rules in which performance is defined by the inclusion of the top-$p$ hypotheses, rather than only the single best or true hypothesis. This criterion is motivated by sensor selection for target tracking, where inexpensive measurements are used to identify a list of sensor nodes that are likely to be closest to a target. We analyze the performance of top-$p$ versus top-$1$ selection under sequential hypothesis testing, propose a geometry-aware sensor selection algorithm, and validate the approach using real testbed data.

In this paper, we consider a multi-armed bandit (MAB) instance and study how to identify the best arm when arm commands are conveyed from a central learner to a distributed agent over a discrete memoryless channel (DMC). Depending on the agent capabilities, we provide communication schemes along with their analysis, which interestingly relate to the zero-error capacity of the underlying DMC.

This paper proposes a novel coding scheme to ensure resilience in millimeter-wave networks, where links are highly sensitive to blockages. The proposed scheme deploys multilevel codes to control the received information and provide different reliability guarantees for different information streams based on their priority. Unlike traditional multilevel coding designs, the proposed scheme maintains low design and operational complexity as the number of paths in the network increases. The achievable rate region of the proposed scheme is characterized and shown to be information-theoretical optimal for the case of two priority levels.

We study a distributed multi-armed bandit (MAB) problem over arm erasure channels, motivated by the increasing adoption of MAB algorithms over communication-constrained networks. In this setup, the learner communicates the chosen arm to play to an agent over an erasure channel with probability$\epsilon \in[0,1)$; if an erasure occurs, the agent continues pulling the last successfully received arm; the learner always observes the reward of the arm pulled. In past work, we considered the case where the agent cannot convey feedback to the learner, and thus the learner does not know whether the arm played is the requested or the last successfully received one. In this paper, we instead consider the case where the agent can send feedback to the learner on whether the arm request was received, and thus the learner exactly knows which arm was played. Surprisingly, we prove that erasure feedback does not improve the worst-case regret upper bound order over the previously studied no-feedback setting. In particular, we prove a regret lower bound of$\Omega(\sqrt{K T}+K /(1-\epsilon))$, where$K$is the number of arms and$T$the time horizon, that matches no-feedback lower bound exactly and upper bound (up to logarithmic factors). We note however that the availability of feedback does enable the design of simpler algorithms that may achieve better constants (albeit not better order) regret bounds; we design one such algorithm, and numerically evaluate its performance.

Quantifying the common information between continuous random sources is fundamental to various applications in machine learning and information theory. Recent work introduced the notion of common information dimension (CID) to measure this. In this paper, we propose a new notion, discrete-to-continuous common information dimension (D2CCID), which characterizes the growth rate of the common information between successively finer quantized sources. As compared to existing CID notions, the proposed notion can be easier to approximate, and is well aligned with common practice in information theory to measure information dimensions. We prove that the proposed measure coincides with existing CID measures for two Gaussian random sources.

Quantifying the common information between random variables is a fundamental problem with a long history in information theory. Traditionally, common information is measured in number of bits and thus such measures are mostly informative when the common information is finite. However, the common information between continuous variables can be infinite; in such cases, a real-valued random vectorWmay be needed to represent the common information, and to be used for instance for distributed simulation. In this paper, we propose the concept of Common Information Dimension (CID) and three variants. We compute the common information dimension for jointly Gaussian random vectors in a closed form. Moreover, we analytically prove, under two different formulations, that the growth rate of common information in the nearly infinite regime is determined by the common information dimension, for the case of two Gaussian vectors.

Achieving ultra-reliable low-latency communications (URLLC) is critical for the operation of data-intensive applications and for ensuring seamless connectivity. Millimeter-wave (mmWave) technology is expected to support URLLC by expanding the available spectrum and providing multi-gigabit services. However, a well-recognized challenge is that mmWave communication links are susceptible to blockage, which may lead to communication disruptions. Conventional approaches, such as interleaving and feedback mechanisms provide resilience against such blockages at the cost of incurring additional delay, which may be too large to support URLLC effectively. This calls for novel techniques to develop resilient transmission mechanisms that can support URLLC. This paper develops gracefully resilient transmission mechanisms by deploying multilevel codes over space and over time. These codes allow the control of the received information and they accommodate different quality of service requirements of different information streams. Our evaluations, carried out also within the ns-3 network simulator, show that deploying these codes leads to attractive trade-offs between rate, delay, and outage probability.

Millimeter-wave (mmWave) spectrum is expected to support data-intensive applications that require ultra-reliable low-latency communications (URLLC). However, mmWave links are highly sensitive to blockage, which may lead to disruptions in the communication. Traditional techniques that build resilience against such blockages (among which are interleaving and feed-back mechanisms) incur delays that are too large to effectively support URLLC. This calls for novel techniques that ensure resilient URLLC. In this paper, we propose to deploy multilevel codes over space and over time. These codes offer several benefits, such as they allow to control what information is received and they provide different reliability guarantees for different information streams based on their priority. We also show that deploying these codes leads to attractive trade-offs between rate, delay, and outage probability. A practically-relevant aspect of the proposed technique is that it offers resilience while incurring a low operational complexity.

In this paper, we are interested in the regime where the common information between two Gaussian random vectors$(X, Y)$can be (or can approach) infinity. We ask two main questions: what is the rate of growth for common information from a finite to an infinite number of bits, as the dependency between the variables increases? and how well can we “approximately” simulate a pair of random variables$(X, Y)$with infinite common information using a finite number of shared bits? We analytically prove that the answer to both of these questions depends on the common information dimension$d(X, Y)$between$X$and$Y$, that we introduced in our recent work [1]. Our work characterizes in a closed form the asymptotic behaviors, by building a connection to singular values associated with the covariance matrix$\Sigma$of$(X, Y)$. We conclude the paper by providing numerical evaluation results that indicate fast convergence to the asymptotic regime.

In this paper, we address the stochastic contextual linear bandit problem, where a decision maker is provided a context (a random set of actions drawn from a distribution). The expected reward of each action is specified by the inner product of the action and an unknown parameter. The goal is to design an algorithm that learns to play as close as possible to the unknown optimal policy after a number of action plays. This problem is considered more challenging than the linear bandit problem, which can be viewed as a contextual bandit problem with a \emph{fixed} context. Surprisingly, in this paper, we show that the stochastic contextual problem can be solved as if it is a linear bandit problem. In particular, we establish a novel reduction framework that converts every stochastic contextual linear bandit instance to a linear bandit instance, when the context distribution is known. When the context distribution is unknown, we establish an algorithm that reduces the stochastic contextual instance to a sequence of linear bandit instances with small misspecifications and achieves nearly the same worst-case regret bound as the algorithm that solves the misspecified linear bandit instances. As a consequence, our results imply a $O(d\sqrt{T\log T})$ high-probability regret bound for contextual linear bandits, making progress in resolving an open problem in Li et al., 2019b, 2021. Our reduction framework opens up a new way to approach stochastic contextual linear bandit problems, and enables improved regret bounds in a number of instances including the batch setting, contextual bandits with misspecifications, contextual bandits with sparse unknown parameters, and contextual bandits with adversarial corruption.

The interference from active to passive users is a well-recognized challenge in millimeter-wave (mmWave) communications. We propose a method that enables to limit the interference on passive users (whose presence may not be detected since they do not transmit) with a small penalty to the throughput of active users. Our approach abstracts away (in a simple, yet informative way) the physical layer component and it leverages the directivity of mmWave links and the available network path diversity. We provide linear programming formulations, lower bounds on active users rates, numerical evaluations, and we establish a connection with the problem of (information theoretically) secure communication over mmWave networks.

Millimeter-wave (mmWave) networks support a large variety of applications, particularly delay-sensitive applications by providing high-speed communication. A well-recognized challenge in mmWave communications is that mmWave links are susceptible to blockage and thus, communication may get disrupted. In this paper, we design and evaluate low-complexity proactive transmission mechanisms for mmWave networks that are resilient to such disruptions. Our mechanisms build on the multipath environment and on the existence of accurate models for link blockage probabilities in mmWave networks. We propose the deployment of symmetric multilevel codes across paths to achieve an attractive trade-off between the average information rate and a graceful performance degradation. Our numerical evaluations show that our proposed coding schemes indeed provide a graceful performance degradation compared to alternative schemes (such as erasure correcting codes), while significantly reducing the code complexity compared to traditional multilevel code designs.

We consider a novel multi-arm bandit (MAB) setup, where a learner needs to communicate the actions to distributed agents over erasure channels, while the rewards for the actions are directly available to the learner through external sensors. In our model, while the distributed agents know if an action is erased, the central learner does not (there is no feedback), and thus does not know whether the observed reward resulted from the desired action or not. We propose a scheme that can work on top of any (existing or future) MAB algorithm and make it robust to action erasures. Our scheme results in a worst-case regret over action-erasure channels that is at most a factor of $O(1/\sqrt {1 - \varepsilon } )$ away from the no-erasure worst-case regret of the underlying MAB algorithm, where ϵ is the erasure probability. We also propose a modification of the successive arm elimination algorithm and prove that its worst-case regret is $\tilde O(\sqrt {KT} + K/(1 - \varepsilon ))$, which we prove is optimal by providing a matching lower bound.

The exact common information between a set of random variables X1,…, Xnis defined as the minimum entropy of a shared random variable that allows for the exact distributive simulation of X1,…, Xn. It has been established that, in certain instances, infinite entropy is required to achieve distributive simulation, suggesting that continuous random variables may be needed in such scenarios. However, to date, there is no established metric to characterize such cases. In this paper, we propose the concept of Common Information Dimension (CID) with respect to a given class of functions ℱ, defined as the minimum dimension of a random variable W required to distributively simulate a set of random variables X1,…, Xn, such that W can be expressed as a function of X1,⋯, Xnusing a member of ℱ. Our main contributions include the computation of the common information dimension for jointly Gaussian random vectors in a closed form, with ℱ being the linear functions class.

Group testing enables to identify infected individuals in a population using a smaller number of tests than individual testing. To achieve this, group testing algorithms commonly assume knowledge of the number of infected individuals; nonadaptive and several adaptive algorithms fall in this category. Some adaptive algorithms, like binary splitting, operate without this assumption, but require a number of stages that may scale linearly with the size of the population. In this paper, we contribute a new algorithm that enables a balance between the number of tests and the number of stages used, and which we term diagonal splitting algorithm (DSA). Diagonal splitting, like binary splitting, does not require knowledge of the number of infected individuals, yet unlike binary splitting, is orderoptimal w.r.t. the expected number of tests it requires and is guaranteed to succeed in a small number of stages that scales at most logarithmically with the size of the population. Numerical evaluations, for diagonal splitting and a hybrid approach we propose, support our theoretical findings.

In this paper, we provide the first efficient batched algorithm for contextual linear bandits with large action spaces. Unlike existing batched algorithms that rely on action elimination, which are not implementable for large action sets, our algorithm only uses a linear optimization oracle over the action set to design the policy. The proposed algorithm achieves a regret upper bound $\tilde{O}(\sqrt{T})$ with high probability, and uses $O(\log\log T)$ batches, matching the lower bound on the number of batches (Gao et al., 2019). When specialized to linear bandits, our algorithm can achieve a high probability gap-dependent regret bound of $\tilde{O}(1/\Delta_{\min})$ with the optimal $\log T$ number of batches, where $\Delta_{\min}$ is the minimum reward gap between a suboptimal arm and the optimal. Our result is achieved via a novel soft elimination approach, that entails $\text{``}$shaping$\text{"}$ the action sets at each batch so that we can efficiently identify (near) optimal actions.

Group testing is a technique that can reduce the number of tests needed to identify infected members in a population, by pooling together multiple diagnostic samples. Despite the variety and importance of prior results, traditional work on group testing has typically assumed independent infections. However, contagious diseases among humans, like SARS-CoV-2, have an important characteristic: infections are governed by community spread, and are therefore correlated. In this paper, we explore this observation and we argue that taking into account the community structure when testing can lead to significant savings in terms of the number of tests required to guarantee a given identification accuracy. To show that, we start with a simplistic (yet practical) infection model, where the entire population is organized in (possibly overlapping) communities and the infection probability of an individual depends on the communities (s)he participates in. Given this model, we compute new lower bounds on the number of tests for zero-error identification and design community-aware group testing algorithms that can be optimal under assumptions. Finally, we demonstrate significant benefits over traditional, community-agnostic group testing via simulations using both noiseless and noisy tests. Shorter versions of this article, which contained a subset of the material, were presented in the work by Nikolopoulos et al. (2021, 2021).

The multi-armed bandit (MAB) problem is an active learning framework that aims to select the best among a set of actions by sequentially observing rewards. Recently, it has become popular for a number of applications over wireless networks, where communication constraints can form a bottleneck. Existing works usually fail to address this issue and can become infeasible in certain applications. In this paper we address the communication problem by optimizing the communication of rewards collected by distributed agents. By providing nearly matching upper and lower bounds, we tightly characterize the number of bits needed per reward for the learner to accurately learn without suffering additional regret. In particular, we establish a generic reward quantization algorithm, QuBan, that can be applied on top of any (no-regret) MAB algorithm to form a new communication-efficient counterpart, that requires only a few (as low as 3) bits to be sent per iteration while preserving the same regret bound. Our lower bound is established via constructing hard instances from a subgaussian distribution. Our theory is further corroborated by numerically experiments.

In this paper, we propose a new federated multi-armed bandit framework with vector rewards that can abstract personalized recommendations. In our setup, each reward is a vector, and each user may be interested in a different dimension of this vector. For example, some users may specifically care about the food quality, service, environment, location, or price, in restaurant recommendations. We propose a Federated Personalized Arm Elimination (FPAE) algorithm and explore two communication constrained scenarios. One scenario allows only one communication round during learning, while the other allows multiple communication rounds. We design two algorithms (FPAE-1 and FPAE-R) for the scenarios and theoretically evaluate their regret. We show that communication can speed up the learning process and that there is a tradeoff between the communication cost and the learning performance as captured by the regret. Numerical analysis results demonstrate the performance of our proposed methods.

Millimeter Wave (mmWave) (and beyond) is expected to play an increasingly important role in our wireless infrastructure by expanding the available spectrum and enabling multi-gigabit services. Despite the promising aspects of mmWave communication, mmWave links are highly sensitive to blockage. In this paper, we develop proactive transmission mechanisms that suitably distribute the traffic across multiple paths in the mmWave network, with the two-fold objective of ensuring resilience against link blockages and achieve high end-to-end packet delivery rate. We present examples of resilience-capacity trade-off curves and show that there exist network topologies for which the worst-case and average approximate capacities are achieved by activating overlapping paths. We also show that this can provide additional benefits, such as decreasing the variance of the achieved rate.

We consider a distributed detection problem where sensors observe dependent observations. We ask, if we can allow the sensors to locally exchange a few bits with each other, whether we can use these bits to "break" the dependency of the sensor observations, and thus reduce the dependent detection problem to the much better-studied and understood case of conditionally independent observations. To this end, we propose an optimization problem that we prove is equivalent to minimizing the dependency between the sensor observations. This problem is in general NP-hard, however, we show that for at least some cases of Gaussian distributions it can be solved efficiently. For general distributions, we propose to use alternating minimization and derive a constant factor approximation algorithm. Numerical evaluations indicate that our approach can offer significant improvement in detection accuracy over alternative schemes.

We study the problem of group testing with non-identical, independent priors. So far, the pooling strategies that have been proposed in the literature take the following approach: a hand-crafted test design along with a decoding strategy is proposed, and guarantees are provided on how many tests are sufficient in order to identify all infections in a population. In this paper, we take a different, yet perhaps more practical, approach: we fix the decoder and the number of tests, and we ask, given these, what is the best test design one could use? We explore this question for the Definite Non-Defectives (DND) decoder. We formulate a (non-convex) optimization problem, where the objective function is the expected number of errors for a particular design. We find approximate solutions via gradient descent, which we further optimize with informed initialization. We illustrate through simulations that our method can achieve significant performance improvement over traditional approaches.

In this paper, we introduce a "discrete-time SIR stochastic block model" that also allows for group testing and interventions on a daily basis. Our model can be regarded as a discrete version of the well-known continuous-time SIR stochastic network model [1] and relies on a specific type of weighted graph to capture the underlying community spread. Given that infection model, we then formulate a dynamic group-testing problem by asking: (a) what is the minimum number of tests needed everyday to identify all infections? and (b) are there nonadaptive group testing strategies that achieve this with vanishing error probability? Our results show that one can leverage the knowledge of the community infection model to compute a lower bound on the number of tests and also inform nonadaptive group testing algorithms, so that they can achieve (almost) the same performance as complete individual testing with a much smaller number of tests. Moreover, these algorithms are order-optimal, under specific conditions.

Contextual linear bandits is a rich and theoretically important model that has many practical applications. Recently, this setup gained a lot of interest in applications over wireless where communication constraints can be a performance bottleneck, especially when the contexts come from a large $d$-dimensional space. In this paper, we consider the distributed contextual linear bandit learning problem, where the agents who observe the contexts and take actions are geographically separated from the learner who performs the learning while not seeing the contexts. We assume that contexts are generated from a distribution and propose a method that uses $\approx 5d$ bits per context for the case of unknown context distribution and $0$ bits per context if the context distribution is known, while achieving nearly the same regret bound as if the contexts were directly observable. The former bound improves upon existing bounds by a $\log(T)$ factor, where $T$ is the length of the horizon, while the latter achieves information theoretical tightness.

In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in disjoint communities: each individual participates in a community, and its infection probability depends on the community (s)he participates in. Use cases include families, students who participate in several classes, and workers who share common spaces. Group testing reduces the number of tests needed to identify the infected individuals by pooling diagnostic samples and testing them together. We show that if we design the testing strategy taking into account the community structure, we can significantly reduce the number of tests needed for adaptive and non-adaptive group testing, and can improve the reliability in cases where tests are noisy.

In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in connected communities: each individual participates in one or more communities, and the infection probability of each individual depends on the communities (s)he participates in. Use cases include students who participate in several classes, and workers who share common spaces. Group testing reduces the number of tests needed to identify the infected individuals by pooling diagnostic samples and testing them together. We show that making testing algorithms aware of the community structure, can significantly reduce the number of tests needed both for adaptive and non-adaptive group testing.

This paper considers benefits of coding techniques in recommendation systems operating over wireless channels with erasures. We identify scenarios where coded broadcasting can increase the overall user satisfaction at a fixed channel utilization level. Such opportunities arise both when user preferences are unknown, and must be explored, and when they are known and must be exploited to recommend optimally. We determine the magnitude of the potential gains and show that coding is most beneficial if users have heterogeneous preferences. Finally, we provide inequalities that can be evaluated to determine whether coding would be beneficial for a certain reward structure.

In this paper, we study the problem of optimal topology design in wireless networks equipped with highly-directional transmission antennas. We use the 1-2-1 network model to characterize the optimal placement of two relays that assist the communication between a source-destination pair. We analytically show that under some conditions on the distance between the source-destination pair, the optimal topology in terms of maximizing the network throughput is to place the relays as close as possible to the source and the destination.

SIR (Susceptible, Infected or Recovered) stochastic network models are commonly used to describe the progression of epidemics inside a network. A task of interest in epidemiology is to use these models to estimate the state evolution, both at an individual as well as a population level. In this paper, we propose using continual testing to improve the state estimation at the individual level. Our testing is inspired from entropy reduction principles and requires only a small number of tests.

Millimeter wave (mmWave) communication is expected to play a central role in next generation mobile systems (5G) and beyond, by providing multi-Gbps data rates. However, the severe pathloss and sensitivity to blockages at mmWave frequencies significantly challenge practical implementations. One effective way to mitigate these effects and to increase the communication range is beamforming in combination with relaying. In this paper, we study the beam scheduling problem for mmWave half-duplex (HD) relay networks, where the relay topology can be arbitrary. Based on theoretically optimal scheduling results, we first implement a network simplification procedure to reduce the network topology complexity, and then propose two practically relevant beam scheduling schemes: the deterministic edge coloring (EC) scheduler and the adaptive backpressure (BP) scheduler. The former consists of a very simple one-time computation of the sequence of scheduling states, which is then repeated periodically. The one-time computation depends on the underlying network topology, and therefore it must be repeated when such topology changes. As such, this approach is more suited to quasi-static scenarios. The latter is an “online” approach which updates scheduling weights and solves at each time slots a weighted sum rate maximization. Hence, it's computational complexity may be significantly higher than that of EC, but it is better suited to dynamic time-varying scenarios. With the aid of computer simulations, we show that both the proposed schedulers guarantee network stability within the network capacity. Particularly, in comparison with two baseline schemes, the proposed schedulers achieve much smaller queuing backlogs, much smaller backlog fluctuations, and much lower packet end-to-end delays.

This paper proposes a new model for wireless relay networks referred to as “1-2-1 network”, where two nodes can communicate only if they point “beams” at each other, otherwise no signal can be exchanged or interference can be generated. This model is motivated by millimeter wave communications where, due to the high path loss, a link between two nodes can exist only if beamforming gain at both sides is established, while in the absence of beamforming gain the signal is received well below the thermal noise floor. The main contributions in this paper include: (a) the development of a constant gap approximation for the unicast and multicast capacities of the proposed network model, i.e., a characterization of the network unicast and multicast capacities to within an additive gap, which only depends on the number of nodes and is independent of the channel coefficients and operating SNR; and (b) the design of algorithms that run in polynomial time in the number of nodes and compute the approximate unicast and multicast capacities, as well as their corresponding optimal beam scheduling strategies. These results are derived both forfull-duplexandhalf-duplexmodes of operation at the relays: while in full-duplex the transmit and receive beams at a relay can be simultaneously active, in half-duplex only one can be active at each point in time. The relation between the approximate multicast capacity and minimum unicast capacity is explored in full-duplex 1-2-1 networks and shown to be dependent on the network structure and the number of destinations, unlike in classical wireless (i.e., without 1-2-1 constraints) full-duplex networks. Finally, network simplification results are proved for the 1-2-1 network model by exploiting the structure of the linear program that represents the approximate capacity.

Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion channels, a notoriously difficult problem due to its highly combinatorial nature. Although works in theoretical computer science have provided algorithms which guarantee perfect reconstruction with multiple independent observations from the deletion channel, they are only applicable in the large blocklength regime and more restrictively, when the number of observations is also large. Indeed, with only a few observations, perfect reconstruction of the input sequence may not even be possible in most cases. In such situations, maximum likelihood (ML) and maximum aposteriori (MAP) estimates for the deletion channels are natural questions that arise and these have remained open to the best of our knowledge. In this work, we take steps to answer the two aforementioned questions. Specifically: 1. We show that solving for the ML estimate over the single deletion channel (which can be cast as a discrete optimization problem) is equivalent to solving its relaxation, a continuous optimization problem; 2. We exactly compute the symbolwise posterior distributions (under some assumptions on the priors) for both the single as well as multiple deletion channels. As part of our contributions, we also introduce tools to visualize and analyze error events, which we believe could be useful in other related problems concerning deletion channels.

Fully autonomous vehicles need the ability to localize without external help, for instance by using visual sensors together with a pre-loaded map of landmarks. In this paper we connect self-localization using landmarks with coding theory. This connection enables to translate Hamming distance properties to probabilistic localization guarantees given a certain number of errors in landmark identification; it also enables to leverage existing polynomial time decoding algorithms for localization. We present promising numerical evaluation results by simulating vehicle traveling paths along a road network generated from real data of a region in Washington D.C.

In this work, we study bounds on the capacity of full-duplex Gaussian 1-2-1 networks with imperfect beamforming. In particular, different from the ideal 1-2-1 network model introduced in [1], in this model beamforming patterns result in side-lobe leakage that cannot be perfectly suppressed. The 1-2-1 network model captures the directivity of mmWave network communications, where nodes communicate by pointing main-lobe "beams" at each other. We characterize the gap between the approximate capacities of the imperfect and ideal 1-2-1 models for the same channel coefficients and transmit power. We show that, under some conditions, this gap only depends on the number of nodes. Moreover, we evaluate the achievable rate of schemes that treat the resulting side-lobe leakage as noise, and show that they offer suitable solutions for implementation.

In this paper we are interested in what we term the federated private bandits framework, that combines differential privacy with multi-agent bandit learning. We explore how differential privacy based Upper Confidence Bound (UCB) methods can be applied to multi-agent environments, and in particular to federated learning environments both in ‘master-worker’ and ‘fully decentralized’ settings. We provide theoretical analysis on the privacy and regret performance of the proposed methods and explore the tradeoffs between these two.

Maximum likelihood (ML) and symbolwise maximum aposteriori (MAP) estimation for discrete input sequences play a central role in a number of applications that arise in communications, information and coding theory. Many instances of these problems are proven to be intractable, for example through reduction to NP-complete integer optimization problems. In this work, we prove that the ML estimation of a discrete input sequence (with no assumptions on the encoder/channel used) is equivalent to the solution of a continuous non-convex optimization problem, and that this formulation is closely related to the computation of symbolwise MAP estimates. This equivalence is particularly useful in situations where a function we term the expected likelihood is efficiently computable. In such situations, we give a ML heuristic and show numerics for sequence estimation over the deletion channel.

This paper studies the problem of secure communication over noiseless 1-2-1 networks, an abstract model for networks with directional communication capabilities such as mmWave networks. A secure transmission scheme is designed and shown to achieve a secure rate that is larger than state-of-the-art lower bounds for a class of 1-2-1 network topologies. The proposed scheme leverages the scheduling nature of 1-2-1 networks, the network topology, as well as storage at intermediate nodes to create shared randomness with the source to improve the secure rate. Finally, a novel outer bound is derived and shown to match the achievability bound under certain network conditions, hence characterizing the secure capacity in such regimes.

This paper investigates the problem of secure communication in a wireline noiseless scenario where a source wishes to communicate to a number of destinations in the presence of a passive external adversary. Different from the multicast scenario, where all destinations are interested in receiving the same message, in this setting different destinations are interested in different messages. The main focus of this paper is on characterizing the secure capacity region, when the adversary has unbounded computational capabilities, but limited network presence. Towards this end, an outer bound on the secure capacity region is derived, and secure transmission schemes are designed and analyzed in terms of achieved rate performance. It is first shown that, for the case of two destinations, the designed scheme matches the outer bound, hence characterizing the secure capacity region. Then, a particular class of networks referred to as two-layer networks is considered, where the source communicates with the destinations by hopping information through one layer of relays. It is shown that the designed scheme is indeed capacity achieving for any two-layer network for which one of the following three conditions is satisfied: (i) the number of destinations is three, (ii) the number of edges eavesdropped by the adversary is one, (iii) the min-cut capacities assume specific values. It is also shown that two-layer networks can be used to model and study a more general class of networks, referred to as separable. The key feature of separable networks is that they can be partitioned into edge disjoint networks that satisfy specific min-cut properties. In particular, it is proved that the secure capacity region of any separable network can be characterized from the secure capacity region of the corresponding two-layer network. Finally, for an arbitrary network topology, a two-phase scheme is designed and its rate performance is compared with the capacity-achieving scheme for networks with two destinations.

This paper investigates the problem of characterizing the capacity of Half-Duplex (HD) line networks, where a source node communicates to a destination node through a multihop path of N relays. If the relays operate in Full-Duplex (FD), it is well known that the capacity of the line network equals the minimum among the point-to-point link capacities in the path. In contrast, this paper considers a different case where the relays operate in HD. In the first part of the paper, it is shown that the approximate capacity (optimal up to a constant additive gap that only depends on the number of nodes in the network) of an HD N-relay line network equals half the minimum of the harmonic means of the point-to-point link capacities of each two consecutive links in the path. It is then proved that the N +1 listen/transmit states (out of the 2Npossible ones) sufficient to characterize the approximate capacity can be found in linear time. In the second part of the paper, it is shown that the problem of finding the path that has the largest HD approximate capacity in a network that can be represented as a graph is NP-hard. However, if the number of cycles in the network is polynomial in the number of nodes, then a polynomial-time algorithm can indeed be designed.

This paper explores the network simplification problem for Gaussian full-duplex relay networks with arbitrary topology. Particularly, given an N-relay Gaussian full-duplex network, the network simplification problem seeks to find fundamental guarantees on the capacity of the best subnetwork, among a particular class of subnetworks, as a fraction of the full-network capacity. The focus of this work is the case when the selected subnetwork class is a path from the source to the destination. The main result of the paper shows that for an N-relay Gaussian networks with arbitrary topology, the best route can in the worst case guarantee an approximate fraction 1/(⌊N/2⌋ + 1) of the capacity of the full network, independently of the channel coefficients and/or operating SNR. Furthermore, this guarantee is shown to be fundamental, i.e., it is the highest worst-case guarantee that can be provided for routing in relay networks. A key step in the proof of the main result lies in the derivation of a simplification result for antenna selection in MIMO channels that may also be of independent interest. To the best of our knowledge, this is the first result that characterizes the performance of routing in comparison to physical layer cooperation techniques that approximately achieve the network capacity for general wireless network topologies. The results in this paper show that routing can, in the worst case, result in an unbounded gap from the network capacity - or reversely, physical layer cooperation can offer unbounded gains over routing.

In the traditional index coding problem, a server employs coding to send messages to a set of clients within the same broadcast domain. Each client already has some messages as side information and requests a particular unknown message from the server. All clients learn the coding matrix so that they can decode and retrieve their requested data. Our starting observation comes from the work by Karmoose et al., which shows that learning the coding matrix can pose privacy concerns: it may enable a client to infer information about the requests and side information of other clients. In this paper, we mitigate this privacy concern by allowing each client to have limited access to the coding matrix. In particular, we design coding matrices so that each client needs only to learn some of (and not all) the rows to decode her requested message. We start by showing that this approach can indeed help mitigate that privacy concern. We do so by considering two different privacy metrics. The first one shows the attained privacy benefits based on a geometric interpretation of the problem. Differently, the second metric, referred to as maximal information leakage, provides upper bounds on: (i) the guessing power of the adversaries (i.e., curious clients) when our proposed approach is employed, and (ii) the effect of decreasing the number of accessible rows on the attained privacy. Then, we propose the use of k-limited-access schemes: given an index coding scheme that employs T transmissions, we create a k-limited-access scheme with Tk≥ T transmissions, and with the property that each client needs at most k transmissions to decode her message. We derive upper and lower bounds on Tkfor all values of k, and develop deterministic designs for these schemes, which are universal, i.e., independent of the coding matrix. We show that our schemes are order-optimal for some parameter regimes, and we propose heuristics that complement the universal schemes for the remaining regimes.

A promising research area that has recently emerged, is on how to use index coding to improve the communication efficiency in distributed computing systems, especially for data shuffling in iterative computations. In this paper, we posit that pliable index coding can offer a more efficient framework for data shuffling, as it can better leverage the many possible shuffling choices to reduce the number of transmissions. We theoretically analyze pliable index coding under data shuffling constraints, and design a hierarchical data-shuffling scheme that uses pliable coding as a component. We find benefits up to O(ns/m) over index coding, where ns/m is the average number of workers caching a message, and m, n, and s are the numbers of messages, workers, and cache size, respectively.

This paper studies the 1-2-1 half-duplex network model, where two half-duplex nodes can communicate only if they point "beams" at each other; otherwise, no signal can be exchanged or interference can be generated. The main result of this paper is the design of two polynomial-time algorithms that: (i) compute the approximate capacity of the 1-2-1 half-duplex network and, (ii) find the network schedule optimal for the approximate capacity. The paper starts by expressing the approximate capacity as a linear program with an exponential number of constraints. A core technical component consists of building a polynomial-time separation oracle for this linear program, by using algorithmic tools such as perfect matching polytopes and Gomory-Hu trees.

This paper studies the multicast capacity of full-duplex 1-2-1 networks. In this model, two nodes can communicate only if they point "beams" at each other; otherwise, no signal can be exchanged. The main result of this paper is that the approximate multicast capacity can be computed by solving a linear program in the activation times of links connecting pairs of nodes. This linear program has two appealing features: (i) it can be solved in polynomial-time in the number of nodes; (ii) it allows to efficiently find a network schedule optimal for the approximate capacity. Additionally, the relation between the approximate multicast capacity and the minimum approximate unicast capacity is studied. It is shown that the ratio between these two values is not universally equal to one, but it depends on the number of destinations in the network, as well as graph-theoretic properties of the network.

In many machine learning applications, once we have learned a classifier, in order to apply it, we may still need to gather features from distributed sensors over communication constrained channels. In this paper, we propose a polynomial complexity algorithm for feature quantization tailored to minimizing the classification error of a linear classifier. Our scheme produces scalar quantizers that are well-tailored to delay-sensitive applications, operates on the same training data used to learn the classifier, and allows each distributed sensor to operate independently of each other. Numerical evaluation indicates up to 65% benefits over alternative approaches. Additionally, we provide an example where, jointly designing the linear classifier and the quantization scheme, can outperform sequential designs.

We consider recommendation systems that need to operate under wireless bandwidth constraints, which is measured as the number of broadcast transmissions. We demonstrate a (tight for some instances) tradeoff between regret and bandwidth for wireless recommendations formulated in a contextual multiarmed bandit framework.

We consider the problem of reconstructing a sequence from fixed number of deleted versions of itself (also called traces). The problem is motivated from recent developments in de novo DNA sequencing technologies. The main contribution of this work is to provide a polynomial time algorithm for symbolwise MAP decoding with multiple traces. The algorithm leverages a dynamic program on the edit graph. We also develop a heuristic with reduced time complexity using similar ideas and provide preliminary numerical evaluations.

This paper studies the problem of information theoretic secure communication when a source has private messages to transmit to m destinations, in the presence of a passive adversary who eavesdrops an unknown set of k edges. The information theoretic secure capacity is derived over unit-edge capacity separable networks, for the cases when k = 1 and m is arbitrary, or m = 3 and k is arbitrary. This is achieved by first showing that there exists a secure polynomial-time code construction that matches an outer bound over two-layer networks, followed by a deterministic mapping between two-layer and arbitrary separable networks.

This paper explores the network simplification problem in the context of Gaussian half-duplex diamond networks. Specifically, given an N-relay diamond network, this problem seeks to derive fundamental guarantees on the capacity of the best k-relay subnetwork, as a function of the full network capacity. Simplification guarantees are presented in terms of a particular approximate capacity, termed Independent-Gaussian (IG) approximate capacity, that characterizes the network capacity to within an additive gap, which is independent of the channel coefficients and operating SNR. The main focus of this work is when k = N-1 relays are selected out of N relays in a diamond network. First, a simple algorithm is proposed which selects all relays except the one with the minimum IG approximate half-duplex capacity. It is shown that the selected (N -1)-relay subnetwork has an IG approximate half-duplex capacity that is at least 1/2 of the IG approximate half-duplex capacity of the full network and that for the proposed algorithm, this guarantee is tight. Furthermore, this work proves the following tight fundamental guarantee: there always exists a subnetwork of k = N - 1 relays that have an IG approximate half-duplex capacity that is at least equal to (N - 1)/N of the IG approximate half-duplex capacity of the full network. Finally, these results are extended to derive lower bounds on the fraction guarantee when k ∈ [1 : N] relays are selected. The key steps in the proofs lie in the derivation of properties of submodular functions, which provide a combinatorial handle on the network simplification problem for Gaussian half-duplex diamond networks.

This paper starts by assuming a 1-2-1 network, the abstracted noiseless model of mmWave networks that was shown to closely approximate the Gaussian capacity in [1], and studies secure communication. First, the secure capacity is derived for 1-2-1 networks where a source is connected to a destination through a network of unit capacity links. Then, lower and upper bounds on the secure capacity are derived for the case when source and destination have more than one beam, which allow them to transmit and receive in multiple directions at a time. Finally, secure capacity results are presented for diamond 1-2-1 networks when edges have different capacities.

This paper proposes a new model for wireless relay networks referred to as “1-2-1 network”, where two nodes can communicate only if they point “beams” at each other, while if they do not point beams at each other, no signal can be exchanged or interference can be generated. This model is motivated by millimeter wave communications where, due to the high path loss, a link between two nodes can exist only if beamforming gain at both sides is established, while in the absence of beamforming gain the signal is received well below the thermal noise floor. The main result in this paper is that the 1-2-1 network capacity can be approximated by routing information along at most 2N + 2 paths, where N is the number of relays connecting a source and a destination through an arbitrary topology.

It was recently observed in [1], that in index coding, learning the coding matrix used by the server can pose privacy concerns: curious clients can extract information about the requests and side information of other clients. One approach to mitigate such concerns is the use of k-limited-access schemes [1], that restrict each client to learn only part of the index coding matrix, and in particular, at most k rows. These schemes transform a linear index coding matrix of rank T to an alternate one, such that each client needs to learn at most k of the coding matrix rows to decode its requested message. This paper analyzes k-limited-access schemes. First, a worst-case scenario, where the total number of clients n is 2T-1 is studied. For this case, a novel construction of the coding matrix is provided and shown to be order-optimal in the number of transmissions. Then, the case of a general n is considered and two different schemes are designed and analytically and numerically assessed in their performance. It is shown that these schemes perform better than the one designed for the case n=2T-1.

The problem of reconstructing a sequence when observed through multiple looks over deletion channels occurs in “de novo” DNA sequencing. The DNA could be sequenced multiple times, yielding several “looks” of it, but each time the sequencer could be noisy with (independent) deletion impairments. The main goal of this paper is to develop reconstruction algorithms for a sequence observed through the lens of a fixed number of deletion channels. We use the probabilistic model of the deletion channels to develop both symbol-wise and sequence maximum likelihood decoding criteria, and algorithms motivated by them. Numerical evaluations demonstrate improvement in terms of edit distance error, over earlier algorithms.

Trade-offs between distributed computation and communication are recently attracting significant interest; however, these works assume that all nodes that share the distributed computation task are within the same broadcast domain, and each can losslessly broadcast to every other node that takes part in the computation task. In this work, we dispose of this assumption, and consider the case where each node can broadcast to a subset of the nodes that take part in the computation task. We model the network via an Erdos-Renyi random graph model where a pair of nodes can communicate with each other with a probability p. We propose both uncoded and coded transmission schemes and give an achievable communication-computation tradeoff for large computational loads.

We consider wireless recommender systems that need to learn the user preferences (explore) and use them to accordingly decide what are the most profitable recommendations to make (exploit), under bandwidth constraints. We propose a graph-based scheme that leverages user side information and coding to efficiently exploit and explore over wireless, and evaluate its performance.

Social groups open up the opportunity for a new form of caching. This paper investigates how a social group of users can jointly optimize bandwidth usage, by each caching network-coded parts of the data demand, and then opportunistically share these parts among themselves upon meeting. First, the problem is formulated as a linear program (LP) with exponential complexity in the number of users. Then, a heuristic algorithm is proposed, which is inspired by the bipartite set-cover problem and operates in polynomial time. For some scenarios, a worst-case performance guarantee of the heuristic with respect to the optimal LP solution is proved. Finally, the performance of the algorithm is assessed using real-world mobility traces synthesized using the SWIM model and from the MIT Reality Mining project data set. The proposed heuristic offers bandwidth savings up to 65% for a waiting time of 30 minutes and up to 28% performance gains with respect to the alternative solutions. These benefits make the algorithm a feasible candidate solution for bandwidth savings.

In pliable index coding, we consider a server withm messages and n clients, where each client has as side information a subset of the messages. We seek to minimize the number of broadcast transmissions, so that each client can recover any one unknown message she does not already have. Previous work has shown that the pliable index coding problem is NP-hard and requires at most O(log2(n)) broadcast transmissions, which indicates exponential savings over the conventional index coding that requires in the worst case O(n) transmissions. In this paper, building on a decoding criterion that we propose, we first design a deterministic polynomial-time algorithm that can realize the exponential benefits, by achieving, in the worst case, a performance upper bounded by O(log2(n)) broadcast transmissions. We extend our algorithm to the t-requests case, where each client requires t unknown messages that she does not have, and show that our algorithm requires at most O(t log(n) + log2(n)) broadcast transmissions. We construct lower bound instances that require at least Ω(log(n)) transmissions for linear pliable index coding and at least Ω(t + log(n)) transmissions for the t-requests case, indicating that both our upper and lower bounds are polynomials of log(n) and differ within a factor of O(log(n)). We provide a probabilistic analysis over random instances and show that the required number of transmissions is almost surely Θ(log(n)), as compared with the Θ(n/ log(n)) for index coding. In addition, we show that these upper and lower bounds also hold for vector pliable index coding in the worst case instances and the random graph instances, implying that vector coding does not provide benefits in terms of these bounds. Our numerical experiments show that our algorithm outperforms existing algorithms for pliable index coding by up to 50% less transmissions.

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

Using a broadcast channel to transmit clients' data requests may impose privacy risks. In this paper, we tackle such privacy concerns in the index coding framework. We show how a curious 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.

This paper asks how much we can gain in terms of bandwidth and user satisfaction, if recommendation systems became bandwidth aware and took into account not only the user preferences, but also the fact that they may need to serve these users under bandwidth constraints, as is the case over wireless networks. We formulate this as a new problem in the context of index coding: we relax the index coding requirements to capture scenarios where each client has preferences associated with messages. The client is satisfied to receive any message she does not already have, with a satisfaction proportional to her preference for that message. We consistently find, over a number of scenarios we sample, that although the optimization problems are in general NP-hard, significant bandwidth savings are possible even when restricted to polynomial time algorithms.

A promising area that has recently emerged, is on how to use index coding to improve the communication efficiency in distributed computing systems, especially for data shuffling in iterative computations. In this paper, we posit that pliable index coding can offer a more efficient framework for data shuffling, as it can better leverage the many possible shuffling choices to reduce the number of transmissions. We theoretically analyze pliable index coding under data shuffling constraints, and design an hierarchical data-shuffling scheme that uses pliable index coding as a component. We find transmission benefits up to O(ns/m) over index coding, where ns/m is the average number of workers caching a message, and m, n, and s are the numbers of messages, workers, and cache size, respectively.

Eavesdropping attacks in inference systems aim to learn not the raw data, but the system inferences to predict and manipulate system actions. We argue that conventional information security measures can be ambiguous on the adversary's estimation abilities, and adopt instead a distortion based framework that enables to operate over a metric space. We show that requiring perfect distortion-based security is more frugal than requiring perfect information-theoretic secrecy even for block length one codes, offering in some cases unbounded gains. Within this framework, we design algorithms that enable to efficiently use shared randomness, and show that each bit of shared random key is exponentially useful in security.

In this paper, we revisit the communication vs. distributed computing trade-off, studied within the framework of MapReduce in [1]. An implicit assumption in the aforementioned work is that each server performs all possible computations on all the files stored in its memory. Our starting observation is that, if servers can compute only the intermediate values they need, then storage constraints do not directly imply computation constraints. We examine how this affects the communication-computation trade-off and suggest that the trade-off be studied with a predetermined storage constraint. We then proceed to examine the case where servers need to perform computationally intensive tasks, and may not have sufficient time to perform all computations required by the scheme in [1]. Given a threshold that limits the computational load, we derive a lower bound on the associated communication load, and propose a heuristic scheme that achieves in some cases the lower bound.

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

In wireless distributed computing, networked nodes perform intermediate computations over data placed in their memory and exchange these intermediate values to calculate function values. In this paper we consider an asymmetric setting where each node has access to a random subset of the data, i.e., we cannot control the data placement. The paper makes a simple point: we can realize significant benefits if we are allowed to be “flexible”, and decide which node computes which function, in our system. We make this argument in the case where each function depends on only two of the data messages, as is the case in similarity searches. We establish a percolation in the behaviour of the system, where, depending on the amount of observed data, by being flexible, we may need no communication at all.

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 the literature for wireless broadcast channels. Here, the main idea is to convert a deterministic channel into multiple independent erasure channels by using superposition coding. For “state-dependent Gaussian” wireless broadcast channels, by using insights from the deterministic problem, we propose an achievability scheme based on a multi-layer wiretap code. By using the wiretap code, we can mimic the phenomenon of converting the wireless channel into multiple independent erasure channels. Then, finding the best achievable secret key generation rate leads to solving a non-convex power allocation problem over these channels (layers). 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.

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.

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 ∈ |1, 2} at least 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.

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 2/(L-1)N+4 (resp. 2/LN+2) 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 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.

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 them 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.

Pliable index coding considers a server with m messages and n clients where each client 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 at most O(log2(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 design a polynomial-time algorithm that uses less than O(log2(n)) transmissions, i.e., almost worst-case optimal. We also establish a connection between the pliable index coding problem and the minrank problem over a family of mixed matrices.

We present protocols for creating pairwise secrets between nodes in a wireless network, so that these secrets are secure from an eavesdropper, Eve, with unbounded computational and memory capabilities, but with limited network presence. We first present a basic secret-agreement protocol for single-hop networks, where secrets are constructed using traffic exchanged between the nodes, and we show that under standard theoretical assumptions, our protocol is information-theoretically secure. Second, we propose a secret-agreement protocol for arbitrary, multi-hop networks that build on the basic protocol but also comprises design features for leveraging additional sources, that multi-hop offers, for secrecy. Finally, we evaluate our protocols, and we provide experimental evidence that it is feasible to create thousands of secret bits per second, in realistic wireless setups, the security of which is independent of Eve’s computational capabilities.

We consider an n-relay Gaussian diamond network where a source communicates to a destination with the help of n half-duplex relays. Achieving rates close to the capacity of this network requires to employ all the n relays under an optimal transmit/receive schedule. Even for the moderate values of n, this can have significant operational complexity as the optimal schedule may possibly have 2ndifferent states for the network (since each of the relays can be in either transmitting or receiving mode). In this paper, we investigate whether a significant fraction of the network capacity can be achieved by using transmit/receive schedules that have only few active states and by using only few relays. First, we conjecture that the approximately optimal schedule has at most n+1 states instead of the 2npossible states. We prove this conjecture for networks of size n ≤ 6 by developing a proof strategy and implementing it computationally. Second, we show that routing strategies that only employ the point-to-point communication and two of the relays with a half-duplex schedule that has only two active states can achieve at least half the capacity (approximately) of the network. Techniques from linear programming and submodular functions are used to derive the results.

This paper presents exact capacity characterizations for the case, when a principal, Alice, wants to securely send a message to another principal, Bob, over three network configurations: the parallel edges network, the V-network, and the triangle network. We assume that: 1) a passive eavesdropper, Eve, overhears any one edge in the network; 2) each edge corresponds to an independent broadcast packet erasure channel with arbitrary erasure probabilities; and 3) all legitimate nodes can publicly but causally acknowledge whether they received each packet or not. We develop optimal achievability schemes that are expressed as linear programs (LPs) and share a two-phase structure, where at the first phase, we create secret keys, and at the second phase, we use them to encrypt the transmitted message. Our outer bounds are also expressed through LP formulations. We prove that our schemes are optimal by showing that the optimal solution of the outer bound LP and the optimal solution of the achievability scheme LP coincide.

We consider a group of mobile users, within proximity of each other, who are interested in watching the same online video. 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) 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 to exchange those parts. Devices cooperate to efficiently utilize all network resources and to adapt to varying wireless network conditions. In the local WiFi network, we exploit overhearing, which we further combine with network coding. The end result is savings in cellular bandwidth and improved user experience. 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 system called MicroCast, and we implement a prototype as an Android application. We provide both simulation results of the NUM solution and experimental evaluation. We demonstrate that the proposed approach brings significant performance benefits (namely, faster download on the order of the group size) without battery penalty.

Linear error correction is widely implemented in millions of telecommunication devices to cope with unreliable or noisy communication channels. A common error in linear encoders is when some bits that are originally one in the generator matrix get erased and become zero - usually due to a soft error becoming a hard error or simply a physical impact on the device. The need to deal with this phenomenon has been recognized in the literature, although to the best of our knowledge no one has ever tried to diagnose erasure-type faults in an encoder. In this paper we focus on the situation when the linear encoder hardware unit becomes faulty and propose a novel combinatorial fault detection scheme based on group testing to diagnose its state with great efficiency in a quick manner. Furthermore we touch upon some solutions to compensate for at both the sender and the receiver side.

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.

One of the most widely-known techniques for securing a message from eavesdropping, is the famous one-time pad. Although the one-time pad offers unconditional security, it has limited applicability today, because it requires that to communicate, two parties already share a key that is not known by the eavesdropper and has size equal to the message. In this review paper we present a line of work that explores how we can efficiently share keys securely from an eavesdropper, and thus communicate using a one-time pad like approach. The basic idea is to exploit new opportunities that wireless networks offer, such as the fact that we have multiple paths, the fact that we have packet losses, and the availability of ACK/NACK feedback.

We formulate a new variant of the index coding problem, where instead of demanding a specific message, clients are pliable, and are interested in receiving any t messages that they do not have. We term this problem pliable index coding or PICOD(t). We prove that, with this formulation, although some instances of the problem become simple, in general, the problem of finding the optimal linear code remains NP-hard. However, we show that it is possible to construct pliable index codes that are substantially smaller than index codes in many cases. If there are n clients, the server has m messages, and each client has a side information set of cardinality s ≤ m - t; we show that O(min{t log n, t + log2n}) broadcast transmissions are sufficient to satisfy all the clients. For t = 1, this is an exponential improvement over the n messages required in index coding in the worst case (for m = n). In addition, for t ≫ log2n, the number of broadcast transmissions required is only linearly dependent on t. We generalize the results to instances where the side information sets are not necessarily of equal cardinality. When m = O(nδ), for some constant δ > 0, we show that the codes of size O(min{t log2n, t log n + log3n}) are sufficient in general. We also consider the scenario when the server only knows the cardinality of the side information sets of the clients and each client is interested in receiving any t messages that it does not have. We term this formulation oblivious pliable index coding or OB-PICOD(t). If the cardinalities of side information sets of all the clients is s (with s ≤ m - t), then we show that min{s + t, m - s} messages are both sufficient and necessary for linear codes. Finally, we develop efficient heuristic approximation algorithms for PICOD(t) and show through simulations on the random instances of PICOD(t) that they perform well in practice.

Secure network coding assumes that the underlying network channels are error-free; thus, if our channels introduce errors, we need to first apply a channel code to correct them, and then build security on top of the resulting error-free network. In this paper, we develop achievability protocols and outer bounds for the secure network coding setting, where the edges are subject to packet erasures, and public feedback of the channel state is available to both Eve and the legitimate network nodes. We show that by leveraging erasures and feedback, we can achieve secrecy rates that are in some cases multiple times higher than the alternative of separate channel-error-correction followed by secure network coding; moreover, we develop outer bounds and prove optimality of our proposed schemes in some special cases.

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 feedback 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 the cases where we have an exact characterization, we can achieve the capacity 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 nonsecure communication problem.

Physical layer cooperation of a source with a relay can significantly boost the performance of a wireless connection. However, the best practical relaying scheme can vary depending on the relative strengths of the channels that connect the source, relay and destination. This paper proposes and evaluates QUILT, a system for physical-layer relaying that seamlessly adapts to the underlying network configuration to achieve competitive or better performance as compared to the best current approaches. QUILT combines on-demand, opportunistic use of Decode-Forward (DF) or Quantize-Map-Forward (QMF) followed by interleaving at the relay, with hybrid decoding at the destination that extracts information from received frames even if these are not decodable. We theoretically quantify how our design choices for QUILT affect the system performance. We also deploy QUILT on the WarpLab software radio platform, and show through over-the-air experiments up to 5 times FER improvement over the next best cooperative protocol.

We consider Gaussian diamond networks with n half-duplex relays. At any point of time, a relay can either be in a listening (L) or transmitting (T) state. The capacity of such networks can be approximated to within a constant gap (independent of channel SNRs) by solving a linear program that optimizes over the 2nrelaying states. We recently conjectured, and proved for the cases of n = 2, 3, that there exist optimal schedules with at most n+1 active states, instead of the possible 2n. In this paper we develop a computational proof strategy that relies on submodularity properties of information flow across cuts in the network and linear programming duality to resolve the conjecture. We implement the strategy for n = 4, 5, 6 and show that indeed there exist optimal schedules with at most n+1 active states in these cases.

We consider a Gaussian diamond network where a source communicates with the destination through n noninterfering half-duplex relays. Using simple approximations to the capacity of the network, we show that simple relaying strategies involving two relays and two scheduling states can achieve at least half the capacity of the whole network, independent of channel SNRs. The proof uses linear programming duality and implies an algorithm to find such a pair of relays in O(n log n) time.

We consider a source that would like to communicate with a destination over a layered Gaussian relay network.We present a computationally efficient method that enables to select a near-optimal (in terms of throughput) subnetwork of a given size connecting the source with the destination. Our method starts by formulating an integer optimization problem that maximizes the rates that the Quantize-Map-and-Forward relaying protocol can achieve over a selected subnetwork; we then relax the integer constraints to obtain a non-linear optimization over reals. For diamond networks, we prove that this optimization over reals is concave while for general layered networks we give empirical demonstrations of near-concavity, paving the way for efficient algorithms to solve the relaxed problem. We then round the relaxed solution to select a specific subnetwork. Simulations using off-the-shelf non-linear optimization algorithms demonstrate excellent performance with respect to the true integer optimum for both diamond networks as well as multi-layered networks. Even with these non-customized algorithms, significant time savings are observed vis-à-vis exhaustive integer optimization.

We characterize the secret message capacity of the triangle network, that consists of a source, a relay and a destination connected through orthogonal erasure channels. A passive eavesdropper, Eve, wiretaps any one of the three channels. The source and the relay can each generate unlimited private randomness; the relay and the destination can publicly provide strictly causal channel state information. Our achievable scheme is expressed through a linear program (LP) with 11 inequalities that captures a minimal set of secret key generation methods and the use of them for message encryption. Our outer bound is expressed also through a linear program, in this case with 41 constraints, constructed from general information inequalities. We prove that the optimal value of the outer bound LP is no larger than that of the scheme LP, which implies that the solution of the achievable scheme LP is the capacity. We find that equipping the relay with private randomness increases the secrecy rate by more than 40% in some cases and that cut-set bounds, directly applied in the network, are not always tight. Because the derivation of the inner and outer bound are both lengthy, we describe in this paper the achievability scheme, outline the outer bound, and provide the full derivations online [1]. We also make available Matlab functions that take as input the erasure probabilities and evaluate the inner and outer bounds.

We consider a Gaussian diamond network where a source communicates with the destination through n non-interfering half-duplex relays. We focus on half-duplex schedules that utilize only local channel state information, i.e., each relay has access to its incoming and outgoing channel realizations. We demonstrate that random independent switching, resulting in multiple listen-transmit sub cycles at each relay, while still respecting the overall locally optimal listen-transmit fractions, enables to approximately achieve at least 3/4 of the capacity of the 2-relay diamond network. With a single listen-transmit cycle, this fraction drops from 3/4 to 1/2. We also provide simulation results that point to the same fractions of capacity being retained over networks with more than 2 relays.

We consider the Gaussian N-relay diamond network, where a source wants to communicate to destination node through a layer of N-relay nodes. We investigate the following question: what fraction of the capacity can we maintain using only k out of the N available relays? We show that independent of the channel configurations and operating SNR, we can always find a subset of k relays, which alone provide a rate k/(k + 1) C̅ - G, where C̅ is the information theoretic cutset upper bound on the capacity of the whole network and G is independent of the channel coefficients and the SNR and depends only on N and k (logarithmic in N and linear in k). In particular, for k = 1, this means that half of the capacity of any N-relay diamond network can be approximately achieved by routing information over a single relay. We also show that this fraction is tight: there are configurations of the N-relay diamond network, where every subset of k relays alone can at most provide approximately a fraction k/(k + 1) of the total capacity. These high-capacity k-relay subnetworks can be also discovered efficiently. We propose an algorithm that computes a constant gap approximation to the capacity of the Gaussian N-relay diamond network in O(N log N) running time and discovers a high-capacity k-relay subnetwork in O(kN) running time. This result also provides a new approximation to the capacity of the Gaussian N-relay diamond network, which is hybrid in nature: it has both multiplicative and additive gaps. In the intermediate SNR regime, this hybrid approximation is tighter than existing purely additive or purely multiplicative approximations to the capacity of this network.

This paper contributes to the design and analysis of Quantize-Map-and-Forward (QMF) relaying by optimizing its performance for small relay networks. QMF was proved to achieve the capacity of arbitrary networks within a bounded gap, as well as the optimal diversity-multiplexing tradeoff over slow fading networks. The initial QMF scheme has each relay performing the same operation, agnostic to the network topology and the channel state information (CSI); this facilitates the analysis for arbitrary networks, yet comes at a performance penalty for small networks and medium SNR regimes. This paper demonstrates the benefits we can gain for QMF if we optimize its performance by leveraging topological and channel state information. We show that for the N-relay diamond network, by taking into account topological information, we can exponentially reduce the QMF additive approximation gap from Θ(N) bits/s/Hz to Θ(log N) bits/s/Hz, while for the one-relay and two-relay networks, use of topological information and CSI can help to gain as much as 6 dB. Moreover, we explore what benefits we can realize if we jointly optimize QMF and half-duplex scheduling, as well as if we employ hybrid schemes that combine QMF and Decode-and-Forward (DF) relay operations.

We consider the problem where a group of wireless nodes, connected to the same broadcast domain, want to create pairwise secrets, in the presence of an adversary Eve, who tries to listen in and steal these secrets. Existing solutions assume that Eve cannot perform certain computations (e.g., large-integer factorization) in useful time. We ask the question: can we solve this problem without assuming anything about Eve's computational capabilities? We propose a simple secret-agreement protocol, where the wireless nodes keep exchanging bits until they have agreed on pairwise secrets that Eve cannot reconstruct with very high probability. Our protocol relies on Eve's limited network presence (the fact that she cannot be located at an arbitrary number of points in the network at the same time), but assumes nothing about her computational capabilities. We formally show that, under standard theoretical assumptions, our protocol is information-theoretically secure (it leaks zero information to Eve about the secrets). Using a small wireless testbed of smart-phones, we provide experimental evidence that it is feasible for 5 nodes to create thousands of secret bits per second, with their secrecy being independent from the adversary's capabilities.

The Pliable Index Coding problem is a recently proposed new formulation of the Index Coding problem where each client wants any one message that it does not have and the server tries to “satisfy” all the clients using the side information sets of each of the clients by broadcasting coded messages. We present two generalizations of the problem. Firstly, we consider the problem of each client requiring any t messages (t ≥ 1) that it does not have. If the cardinality of their side information sets is the same and there are n messages, then we show that O(min(t log n, t + log2n)) coded broadcast messages are sufficient. For t ≥ log n, this shows a linear dependence on t independent of n. We also develop simple approximation algorithms for the problem and evaluate their performance through simulations. Secondly, we consider the problem of the server having incomplete side information. If the server only knows the size s of the side information sets (assumed to be all equal), we show that there exists a linear code using min(s + 1, n - s) coded messages. We also show that this is tight for linear codes by proving a matching lower bound.

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.

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.

We investigate the problem of secure communication in a simple network with three communicating parties, two distributed sources who communicate over orthogonal channels to one destination node. The cooperation between the sources is restricted to a rate limited common random source they both observe. The communication channels are erasure channels with strictly causal channel state information of the destination available publicly. A passive adversary is present in the system eavesdropping on any one of the channels. We design a linear scheme that ensures secrecy against the eavesdropper. By deriving an outer bound for the problem we prove that the scheme is optimal in certain special cases.

Current security systems often rely on the adversary's computational limitations. Wireless networks offer the opportunity for a different, complementary kind of security, which relies on the adversary's limited network presence (i.e., that the adversary cannot be located at many different points in the network at the same time). We present a system that leverages this opportunity to enable n wireless nodes to create a shared secret S, in a way that an eavesdropper, Eve, obtains very little information on S. Our system consists of two steps: (1) The nodes transmit packets following a special pattern, such that Eve learns very little about a given fraction of the transmitted packets. This is achieved through a combination of beam forming (from many different sources) and wiretap codes. (2) The nodes participate in a protocol that reshuffles the information known to each node, such that the nodes end up sharing a secret that Eve knows very little about. Our protocol is easily implementable in existing wireless devices and scales well with the number of nodes; these properties are achieved through a combination of public feedback, broadcasting, and network coding. We evaluate our system through a 5-node testbed. We demonstrate that a group of wireless nodes can generate thousands of new shared secret bits per second, with their secrecy being independent of the adversary's computational capabilities.

We present the design and experimental evaluation of a wireless system that exploits relaying in the context of WiFi. We opt for WiFi given its popularity and wide spread use for a number of applications, such as smart homes. Our testbed consists of three nodes, a source, a relay and a destination, that operate using the physical layer procedures of IEEE802.11. We deploy three main competing strategies that have been proposed for relaying, Decode-and-Forward (DF), Amplify-and-Forward (AF) and Quantize-Map-Forward (QMF). QMF is the most recently introduced of the three, and although it was shown in theory to approximately achieve the capacity of arbitrary wireless networks, its performance in practice had not been evaluated. We present in this work experimental results---to the best of our knowledge, the first ones---that compare QMF, AF and DF in a realistic indoor setting. We find that QMF is a competitive scheme to the other two, offering in some cases up to 12% throughput benefits and up to 60% improvement in frame error-rates over the next best scheme.

Network tomography aims at inferring internal network characteristics based on measurements at the edge of the network. In loss tomography, in particular, the characteristic of interest is the loss rate of individual links and multicast and/or unicast end-to-end probes are typically used. Independently, recent advances in network coding have shown that there are advantages from allowing intermediate nodes to process and combine, in addition to just forward, packets. In this paper, we study the problem of loss tomography in networks with network coding capabilities. We design a framework for estimating link loss rates, which leverages network coding capabilities, and we show that it improves several aspects of tomography, including the identifiability of links, the trade-off between estimation accuracy and bandwidth efficiency, and the complexity of probe path selection. We discuss the cases of inferring link loss rates in a tree topology and in a general topology. In the latter case, the benefits of our approach are even more pronounced compared to standard techniques but we also face novel challenges, such as dealing with cycles and multiple paths between sources and receivers. Overall, this work makes the connection between active network tomography and network coding.

Designing a communication protocol for sensor networks often involves obtaining the right trade-off between energy efficiency and end-to-end packet error rate. In this article, we show that network coding provides a means to elegantly balance these two goals. We present the design and implementation of SenseCode, a collection protocol for sensor networks—and, to the best of our knowledge, the first such implemented protocol to employ network coding. SenseCode provides a way to gracefully introduce a configurable amount of redundant information into the network, thereby decreasing end-to-end packet error rate in the face of packet loss. We compare SenseCode to the best (to our knowledge) existing alternative and show that it reduces end-to-end packet error rate in highly dynamic environments, while consuming a comparable amount of network resources. We have implemented SenseCode as a TinyOS module and evaluate it through extensive TOSSIM simulations.

Current security systems typically rely on the adversary's computational limitations (e.g., the fact that it cannot invert a hash function or perform large-integer factorization). Wireless networks offer the opportunity for a different, complementary kind of security, which relies not on the adversary's computational limitations, but on its limited network presence (i.e., that the adversary cannot be located at many different points in the network at the same time). We take a first step toward designing and building a wireless security system that leverages this opportunity: We consider the problem where a group of n nodes, connected to the same broadcast wireless network, want to agree on a shared secret (e.g., an encryption key), in the presence of an adversary Eve who tries to listen in and steal the secret. We propose a secret-agreement protocol, where the n nodes of the group keep exchanging bits until they have all agreed on a bit sequence that Eve cannot reconstruct (with very high probability). We provide experimental evidence---to the best of our knowledge, the first one---that a group of wireless nodes can generate thousands of new shared secret bits per second, with their secrecy being independent of the adversary's computational capabilities.

In this paper, some novel results on the encoding complexity of network coding and its relation with the network topology are reported. The encoding complexity in network coding is defined as the number of nodes which have to perform coding operations in order to achieve the multicast capacity. These nodes are referred to as coding points. Known results state that the number of coding points is cubic in the mincut and quadratic in the number of receivers. In this paper, we show, through extensive simulations and through analysis of these results, that the number of coding points tends to increase linearly in the min-cut and the number of receivers in random graphs. We show that this is correlated to the length of path from the source to the receivers. To verify this, we also analyze pseudo-random graphs with a larger path length.

We propose a new formulation of the index coding problem, where instead of demanding a specific bit (or message), clients are “pliable” and are happy to receive any one bit they do not have. We prove that with this relaxation, although some instances of this problem become simple, in general the problem of finding the optimal linear code remains NP-hard. We also show that if the server has n bits, O(log n log(n/log n)) coded bit transmissions are sufficient to satisfy the clients in the worst case, in contrast to the Ω(n) transmissions required in index coding. We develop several approximation algorithms and evaluate their performance through simulations.

Abstract—We consider the diamond network where a source communicates with the destination through N non-interfering half-duplex relays. Using simple outer bounds on the capacity of the network, we show that simple relaying strategies having exactly two states and avoiding broadcast and multiple access communication can still achieve a significant constant fraction of the capacity of the 2 relay network, independent of the SNR values. The results are extended to the case of 3 relays for the special class of antisymmetric networks. We also study the structure of (approximately) optimal relaying strategies for such networks. Simulations show that optimal schedules have at most N +1 states, which we conjecture to be true in general. We prove the conjecture for N =2and in special cases for N =3. I.

Consider a source, Alice, broadcasting private messages to multiple receivers through a broadcast erasure channel; users send back to Alice public feedback that she causally uses to decide the coding strategy for her following transmissions. Recently, the multiple unicast capacity region for this problem has been exactly characterized for a number of special cases; namely the 2-user, 3-user, symmetric K-user, and one-sidedly fair K-user [1], [2]. In this paper, we show that for all the cases where such characterizations exist, we can also optimally characterize the “secure” communication rates, where the message that Alice transmits to each user is information theoretically secure from the other users, even if these collude. We show that a simple, two-phase strategy, where appropriate amounts of secret keys are first generated and then consumed, matches a new outer bound we derive.

It is well known that transfer polynomials play an important role in the network code design problem. In this paper we provide a graph theoretical description of the terms of such polynomials. We consider acyclic networks with arbitrary number of receivers and min-cut h between each source-receiver pair. We show that the associated polynomial can be described in terms of certain subgraphs of the network.

We present a method to integrate the Quantize-Map-Forward (QMF) relaying scheme [1] into the standard LTE operation, for a two-relay diamond network configuration. Our approach implements QMF using mainly existing LTE modules and functionalities, and results in minimal changes in the standard link-layer LTE operation. In particular, the destination operation is only affected in that we adapt the log-likelihood ratio (LLR) calculations at the decoder input to take into account the existence of relays; thus, the decoding complexity and operations (apart the LLR calculations) are not modified. We report extensive performance evaluations of our scheme using the OpenAirInterface (OAI) link-level simulation tools.

We evaluate the information-theoretic achievable rates of Quantize-Map-and-Forward (QMF) relaying schemes over Gaussian N-relay diamond networks. Focusing on vector Gaussian quantization at the relays, our goal is to understand how close to the cutset upper bound these schemes can achieve in the context of diamond networks, and how much benefit is obtained by optimizing the quantizer distortions at the relays. First, with noise-level quantization, we point out that the worst-case gap from the cutset upper bound is (N + log2N) bits/s/Hz. A better universal quantization level found without using channel state information (CSI) leads to a sharpened gap of log2N + log2(1 + N) + N log2(1 + 1/N) bits/s/Hz. On the other hand, it turns out that finding the optimal distortion levels depending on the channel gains is a non-trivial problem in the general N-relay setup. We manage to solve the two-relay problem and the symmetric N-relay problem analytically, and show the improvement via numerical evaluations both in static as well as slow-fading channels.

Video streaming is one of the increasingly popular, as well as demanding, applications on smartphones today. In this paper, we consider a group of smartphone users, within proximity of each other, who are interested in watching the same video from the Internet at the same time. The common practice today is that each user downloads the video independently using her own cellular connection, which often leads to poor quality.

In this work, we are interested in a scenario where a group of smartphone users, within proximity of each other, are interested in watching the same video at the same time. The default operation today is that each user with a cellular connection downloads the video independently from the server. However, each phone's individual cellular connection may not be sufficient for providing high video quality.

A long-standing open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts the signals and there is interference among transmissions. Recently, Avestimehr et al. [2007b] proposed a linear deterministic model that takes into account the shared nature of wireless channels, focusing on the signal interactions rather than the background noise. They generalized the min-cut max-flow theorem for graphs to networks of deterministic channels and proved that the capacity can be achieved using information theoretical tools. They showed that the value of the minimum cut is in this case the minimum rank of all the adjacency matrices describing source-destination cuts. In this article, we develop a polynomial-time algorithm that discovers the relay encoding strategy to achieve the min-cut value in linear deterministic (wireless) networks, for the case of a unicast connection. Our algorithm crucially uses a notion of linear independence between channels to calculate the capacity in polynomial time. Moreover, we can achieve the capacity by using very simple one-symbol processing at the intermediate nodes, thereby constructively yielding finite-length strategies that achieve the unicast capacity of the linear deterministic (wireless) relay network.

Systems that employ network coding for content distribution convey to the receivers linear combinations of the source packets. If we assume randomized network coding, during this process, the network nodes collect random subspaces of the space spanned by the source packets. We establish several fundamental properties of the random subspaces induced in such a system and show that these subspaces implicitly carry topological information about the network and its state that can be passively collected and inferred. We leverage this information toward a number of applications that are interesting in their own right, such as topology inference, bottleneck discovery in peer-to-peer systems, and locating Byzantine attackers. We thus argue that randomized network coding, apart from its better known properties for improving information delivery rate, can additionally facilitate network management and control.

We consider communication of two degraded message sets over graphs where a common source sends two prioritized messages (a common and a private message) to several receivers. All receivers require the common message and a subset of the receivers require both the common and private messages. In this paper, we consider the case where all but two of the receivers require both messages. We provide an outer-bound on the rate region that depends on graph properties. We prove that this bound is achievable by using carefully selected linear operations at the network nodes. The achievability proof is built on our result in [14] and is illustrating potential connections of communication over deterministic channels and communication over graphs.

We consider the N-relay Gaussian diamond network when the source and the destination have ns≥ 2 and nd≥ 2 antennas respectively. We show that when ns= nd= 2 and when the individual MISO channels from the source to each relay and the SIMO channels from each relay to the destination have the same capacity, there exists a two relay sub-network that achieves approximately all the capacity of the network. To prove this result, we establish a simple relation between the joint entropies of three Gaussian random variables, which is not implied by standard Shannon-type entropy inequalities.

We consider the Gaussian N-relay diamond network, where a source wants to communicate to a destination node through a layer of N-relay nodes. We investigate the following question: What fraction of the capacity can we maintain by using only k out of the N available relays? We show that in every Gaussian N-relay diamond network, there exists a subset of k relays which alone provide approximately k/k+1 of the total capacity. The result holds independent of the number of available relay nodes N, the channel configurations and the operating SNR. The result is tight in the sense that there exists channel configurations for N-relay diamond networks, where every subset of k relays can provide at most k/k+1 of the total capacity. The approximation is within 3 logN + 3k bits/s/Hz to the capacity. This result also provides a new approximation to the capacity of the Gaussian N-relay diamond network which is up to a multiplicative gap of 1/k+1 and additive gap of 3 logN + 3k. The current approximation results in the literature either aim to characterize the capacity within an additive gap by allowing no multiplicative gap or vice a versa. Our result suggests a new approximation approach where multiplicative and additive gaps are allowed simultaneously and are traded through an auxiliary parameter.

We consider a group of m trusted nodes that aim to create a shared secret key K, using a state-dependent wireless broadcast channel that exists from one of the honest nodes to the rest of the nodes including a passive eavesdropper Eve. All of the trusted nodes can also discuss over a cost-free and unlimited rate public channel which is also observed 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 as well as in the high-SNR regime for wireless channels with large dynamic range over channel states.

We characterize the secret message capacity of a wiretapped erasure channel where causal channel state information of the honest nodes is publicly available. In doing so, we establish an intimate connection between message secrecy and secret key generation for the same channel setup. We propose a linear coding scheme that has polynomial encoding/decoding complexity, and prove a converse that shows the optimality of our scheme. Our work also demonstrates the value of causal public feedback, which has previously been shown for the secret key generation problem.

We present a structured Quantize-Map-and-Forward (QMF) scheme for cooperative communication over wireless networks, that employs LDPC ensembles for the node operations and message-passing algorithms for decoding. We demonstrate through extensive simulation results over the full-duplex parallel relay network, that our scheme, with no transmit channel state information, offers a robust performance over fading channels and achieves the full diversity order of our network at moderate SNRs.

The placement of replicas across storage nodes in a replication-based storage system is known to affect rebuild times and therefore system reliability. Earlier work has shown that, for a replication factor of two, the reliability is essentially unaffected by the replica placement scheme because all placement schemes have mean times to data loss (MTTDLs) within a factor of two for practical values of the failure rate, storage capacity, and rebuild bandwidth of a storage node. However, for higher replication factors, simulation results reveal that this no longer holds. Moreover, an analytical derivation of MTTDL becomes intractable for general placement schemes. In this paper, we develop a theoretical model that is applicable for any replication factor and provides a good approximation of the MTTDL for small failure rates. This model characterizes the system behavior by using an analytically tractable measure of reliability: the probability of the shortest path to data loss following the first node failure. It is shown that, for highly reliable systems, this measure approximates well the probability of all paths to data loss after the first node failure and prior to the completion of rebuild, and leads to a rough estimation of the MTTDL. The results obtained are of theoretical and practical importance and are confirmed by means of simulations. As our results show, the declustered placement scheme, contrary to intuition, offers a reliability for replication factors greater than two that does not decrease as the number of nodes in the system increases.

This paper experimentally studies the reliability and delay of flooding based multicast protocols for a sniper detection application. In particular using an emulator it studies under which conditions protocols based on network coding deliver performance improvements compared to classic flooding. It then presents an implementation of such protocols on mobile phones.

Network coding enables novel network functionalities and thus offers a wider canvas of choices when optimizing an information flow problem. In this paper, we examine the simplest possible information flow problem, a unicast connection, and explore what we believe is one of the most attractive features network coding offers: the ability to enable near-optimal performance in a completely decentralized and randomized setting. This is an especially attractive feature for wireless applications. However, it comes at the cost of an overhead in terms of rate that can be significant for applications that operate using relatively short frame lengths, as is the case in the wireless setting. We review the efforts in the literature to either alleviate this overhead, or alternatively, to exploit it for network management and control.

We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L × L coding matrices that play a similar role as coding coefficients in scalar coding. We start our work by extending the algebraic framework developed for multicasting over graphs by Koetter and Medard to include operations over matrices; we build on this generalized framework, to provide a new approach for both scalar and vector code design which attempts to minimize the employed field size and employed vector length, while selecting the coding operations. Our algorithms also lead as a special case to network code designs that employ structured matrices.

In this paper, we study a Gaussian relay-interference network, in which relay (helper) nodes are to facilitate competing information flows between different source-destination pairs. We focus on two-stage relay-interference networks where there are weak cross links, causing the networks to behave like a chain ofZGaussian channels. Our main result is an approximate characterization of the capacity region for such ZZ and ZS networks. We propose a new interference management scheme, termed interference neutralization, which is implemented using structured lattice codes. This scheme allows for over-the-air interference removal, without the transmitters having complete access the interfering signals. This scheme in conjunction a new network decomposition technique provides the approximate characterization. Our analysis of these Gaussian networks is based on insights gained from an exact characterization of the corresponding linear deterministic model.

We consider the problem of multicasting information from a source to a set of receivers over a network where intermediate network nodes perform randomized linear network coding operations on the source packets. We propose a channel model for the noncoherent network coding introduced by Koetter and Kschischang in , that captures the essence of such a network operation, and calculate the capacity as a function of network parameters. We prove that use of subspace coding is optimal, and show that, in some cases, the capacity-achieving distribution uses subspaces of several dimensions, where the employed dimensions depend on the packet length. This model and the results also allow us to give guidelines on when subspace coding is beneficial for the proposed model and by how much, in comparison to a coding vector approach, from a capacity viewpoint. We extend our results to the case of multiple source multicast that creates a virtual multiple access channel.

We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L × L coding matrices that play a similar role as coding coefficients in scalar coding. Our algorithms for scalar network jointly optimize the employed field size while selecting the coding coefficients. Similarly, for vector coding, our algorithms optimize the length L while designing the coding matrices. These algorithms apply both for regular network graphs as well as linear deterministic networks.

This paper considers function computation in a network where intermediate nodes perform randomized network coding, through appropriate choice of the subspace codebooks at the source nodes. Unlike traditional network coding for computing functions, that requires intermediate nodes to be aware of the function to be computed, our designs are transparent to the intermediate node operations.

Replication is a widely used method to protect large-scale data storage systems from data loss when storage nodes fail. It is well known that the placement of replicas of the different data blocks across the nodes affects the time to rebuild. Several systems described in the literature are designed based on the premise that minimizing the rebuild times maximizes the system reliability. Our results however indicate that the reliability is essentially unaffected by the replica placement scheme. We show that, for a replication factor of two, all possible placement schemes have mean times to data loss (MTTDLs) within a factor of two for practical values of the failure rate, storage capacity, and rebuild bandwidth of a storage node. The theoretical results are confirmed by means of event-driven simulation. For higher replication factors, an analytical derivation of MTTDL becomes intractable for a general placement scheme. We therefore use one of the alternate measures of reliability that have been proposed in the literature, namely, the probability of data loss during rebuild in the critical mode of the system. Whereas for a replication factor of two this measure can be directly translated into MTTDL, it is only speculative of the MTTDL behavior for higher replication factors. This measure of reliability is shown to lie within a factor of two for all possible placement schemes and any replication factor. We also show that for any replication factor, the clustered placement scheme has the lowest probability of data loss during rebuild in critical mode among all possible placement schemes, whereas the declustered placement scheme has the highest probability. Simulation results reveal however that these properties do not hold for the corresponding MTTDLs for a replication factor greater than two. This indicates that some alternate measures of reliability may not be appropriate for comparing the MTTDL of different placement schemes.

In a significant class of sensor-network applications, the identities of the reporting sensors constitute the bulk of the communicated data, whereas the message itself can be as small as a single bit - for instance, in many cases, sensors are used to detect whether and where a certain interesting condition occurred, or to track incremental environmental changes at fixed locations. In such scenarios, the traditional network-protocol paradigm of separately specifying the source identity and the message in distinct fields leads to inefficient communication. This work addresses the question of how communication should happen in such identity-aware sensor networks. We calculate theoretical performance bounds for this type of communication, where 'performance' refers to the number of transmitted bits. We propose a communication protocol, where the identity and message of each source are specified jointly using subspace coding. We show through analysis and simulation that our protocol's performance is close to optimal and compare it to the performance of a traditional protocol, where identity and message are specified separately.

Communication complexity - the minimum amount of communication required - for computing a function of data held by several parties is studied. A communication model where silence is used to convey information is introduced. For this model the worst case and average-case complexities of symmetric functions are studied. For binary-input functions the average- and worst case complexities are determined and the protocols achieving them are described. For functions of nonbinary inputs one-round communication, where each party is restricted to communicate in consecutive stages, is considered and the extra amount of communication required by one- over multiple-round communication is analyzed. For the special case of ternary-input functions close lower and upper bounds on the worst case one-round complexity are provided and protocols achieving them are described. Protocols achieving the average-case one-round complexity for ternary-input functions are also described. These protocols can be generalized to inputs of arbitrary size.

In a significant class of sensor-network applications, the identities of the reporting sensors constitute the bulk of the communicated data, whereas the message itself can be as small as a single bit - for instance, in many cases, sensors are used to detect whether and where a certain interesting condition occured, or to track incremental environmental changes at fixed locations. In such scenarios, the traditional network-protocol paradigm of separately specifying the source identity and the message in distinct fields leads to inefficient communication. This work addresses the question of how should communication happen in such identity-aware sensor networks. We reexamine the traditional source-identity/message separation and propose a scheme for jointly encoding the two. We use this to develop a communication method for identity-aware sensor networks and show it to be energy efficient, simple to implement, and gracefully adaptable to scenarios frequently encountered in sensor networks - for instance, node failures, or large numbers of nodes where only few are active during each reporting round.

We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of mu messages to several receivers over separate erasure channels. The sender can broadcast a single message or a combination (encoding) of messages at each timestep. Receivers provide feedback as to whether the transmission was received. If at some time step a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by real-time applications that request progressively refined input, such as the successive refinement of an image encoded using multiple description coding. Our setup is novel because it combines coding techniques with feedback information to the end of minimizing delay. It allows Theta(mu) benefits as compared to previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay than online algorithms without feedback. Our main complexity results are that the offline minimization problem is NP-hard when the sender only schedules single messages and that the general problem remains NP-hard even when coding is allowed. However we show that coding does offer delay and complexity gains over scheduling. We also discuss online heuristics and evaluate their performance through simulations.

In networks that employ network coding, two main approaches have been proposed in the literature to allow the receivers to recover the source information: (i) use of coding vectors, that keep track of the linear combinations the received packets contain, and (ii) subspace coding, that dispenses of the need to know the linear combinations, since information is conveyed from the choice of subspaces alone. Both these approaches impose the strong requirement that all source packets get potentially combined. We here present a third approach that relaxes this assumption, and is thus not a special case from either of the previous two. This relaxation allows to employ compressed coding vectors to efficiently convey the coding coefficients, without altering the operation of intermediate network nodes. We develop optimal designs for such vectors.

The min-cut value towards a single receiver in a network with unit capacity edges can be achieved by routing a single bit. The multicast theorem in network coding shows that, the common min-cut value towards N ¿ 1 receivers can also be achieved using packets of length logN bits, if the operations the intermediate nodes perform are deterministically known at the receivers. We here calculate the capacity in the case where these operations are unknown, and characterize how the capacity depends on the min-cut value and the packet length.

The wireless multiple-unicast problem is considered over a layered network, where the rates of transmission are limited by the relaying and interference effect. The deterministic model introduced is used to capture the broadcasting and multiple access effects. The capacity region of the Z-chain relay-interference network is fully characterized. In order to solve the problem, we introduce a new achievability scheme based on ldquointerference neutralizationrdquo and a new analysis technique to bound the number of non-interfering (pure) signals.

We consider multisource non-coherent network coding, where multiple sources send information to one or multiple receivers. We prove that this is equivalent to a ldquosubspacerdquo channel, that takes subspaces as inputs and outputs. We then show that the rate of each individual receiver is upper bounded as deltai(T - delta1- delta2), where deltaiis what we define to be the ldquodominatingrdquo dimension in the subspace codebook of source i, and T is the ldquocoherencerdquo time of the network.

A long-standing open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts the signals and there is interference among transmissions. Recently, Avestimehr, Diggavi and Tse proposed a linear binary deterministic model that takes into account the shared nature of wireless channels, focusing on the signal interactions rather than the background noise. They generalized the min-cut max-flow theorem for graphs to networks of deterministic channels and proved that the capacity can be achieved using information theoretical tools. They showed that the value of the minimum cut is in this case the minimum rank of all the binary adjacency matrices describing source-destination cuts. However, since there exists an exponential number of cuts, identifying the capacity through exhaustive search becomes infeasible. In this paper, we develop a polynomial time algorithm that discovers the relay encoding strategy to achieve the min-cut value in binary linear deterministic (wireless) networks, for the case of a unicast connection. Our algorithm crucially uses a notion of linear independence between edges to calculate the capacity in polynomial time. Moreover, we can achieve the capacity by using very simple one-bit processing at the intermediate nodes, thereby constructively yielding finite length strategies that achieve the unicast capacity of the linear deterministic (wireless) relay network.

We examine the problem of multiple sources transmitting information to one or more receivers that require the information from all the sources, over a network where the network nodes perform randomized network coding. We consider the noncoherent case, where neither the sources nor the receivers have any knowledge of the intermediate nodes operations. We formulate a model for this problem, inspired from block- fading noncoherent MIMO communications. We prove, using information theoretic tools, that coding over subspaces is sufficient to achieve the capacity, and give bounds for the capacity. We then examine the associated combinatorial problem of code design. We extend the work by Koetter and Kschischang [3] to code constructions for the multisource case. Our constructions can also be viewed as coding for the noncoherent multiple-access finite-field channel.

Network tomography infers internal network characteristics by sending and collecting probe packets from the network edge. Traditional tomographic techniques for general topologies typically use a mesh of multicast trees and/or unicast paths to cover the entire graph, which is suboptimal from the point of view of bandwidth efficiency and estimation accuracy. In this paper, we investigate an active probing method for link loss inference in a general topology, where multiple sources and receivers are used and intermediate nodes are equipped with network coding, in addition to unicast and multicast, capabilities. With our approach, each link is traversed by exactly one packet, which is in general a linear combination of the original probes. The receivers infer the loss rate on all links by observing not only the number but also the contents of the received probes. In this paper: (i) we propose an orientation algorithm that creates an acyclic graph with the maximum number of identifiable edges (ii) we define probe combining coding schemes and discuss some of their properties and (iii) we present simulation results over realistic topologies using Belief-Propagation (BP) algorithms.

Communication complexity of computing functions using unrestricted communication and one-round communication are compared. In the standard unrestricted communication each party could potentially communicate several times while in one-round communication each party is restricted to communicate at most once. Results on the ratio of these two complexities are provided for symmetric and asymmetric functions under different scenarios. These results are suitably illustrated with examples.

We propose a mechanism for reliable broadcasting in wireless networks, that consists of two components: a method for bandwidth efficient acknowledgment collection, and a coding scheme that uses acknowledgments. Our approach combines ideas from network coding and distributed space time coding.

Randomized network coding has network nodes randomly combine and exchange linear combinations of the source packets. A header appended to the packet, called coding vector, specifies the exact linear combination that each packet carries. The main contribution of this work is to investigate properties of the subspaces spanned by the collected coding vectors in each network node. We use these properties to exhibit the relationship between the network topology and the subspaces collected at the nodes. This allows us to passively infer the network topology for a general class of graphs.

We consider communication through a cascade of discrete memoryless channels (DMCs). The source and destination node of this cascade are allowed to use coding schemes of arbitrary complexity, but the intermediate relay nodes are restricted to process only blocks of a fixed length. We investigate how the processing at the relays must be chosen in order to maximize the capacity of the cascade, that is, the maximum achievable end-to-end rate between the source and the destination. For infinite cascades with fixed intermediate processing length at the relays, we prove that this intermediate processing can be chosen to be identical without loss of optimality, and that the capacity of the cascade coincides with the rate of the best zero-error code of length equal to the block length of the intermediate processing. We further show that for fixed and identical intermediate processing at all relays, convergence of capacity as the length of the cascade goes to infinity is exponentially fast. Finally, we characterize how the block length of the intermediate processing must scale with the length of the cascade to guarantee a constant end-to-end rate. We prove that it is sufficient that the block length scales logarithmically with the network length in order to achieve any rate above the zero-error capacity. We show that in many cases of interest logarithmic growth is also necessary.

Abstract — We show that network coding allows to realize en-ergy savings in a wireless ad-hoc network, when each node of the network is a source that wants to transmit information to all other nodes. Energy efficiency directly affects battery life and thus is a critical design parameter for wireless networks. We propose an implementable method for performing network coding in such a setting. We analyze theoretical cases in detail, and use the insights gained to propose a practical, fully distributed method for realistic wireless ad-hoc scenarios. We address practical issues such as setting the forwarding factor, managing generations, and impact of transmission range. We use theoretical analysis and packet level simulation. I.

A non-uniform demand network consists of a source and a set of receivers that have different min-cut values from the source. We look at the case where each receiver would like to receive information from the source at a rate that is equal to its min-cut value. This problem has been formulated before, and in contrast to the uniform case, it has been shown that the non-uniform case does not admit a good characterization. Motivated by this, we formulate relaxations of the problem and present some preliminary results

We consider a power-efficient communication model for wireless sensor networks where silence is used to convey information. We study the average-case and worst-case complexities of symmetric functions under this model and describe protocols that achieve them. For binary-input functions, we determine the average complexity. For ternary-input functions, we consider a special type of protocols and provide close lower and upper bounds for their worst-case complexity. We also describe the protocol that achieves the average complexity

We consider communication through a cascade of L identical discrete memoryless channels (DMCs). The source and destination node are allowed to use coding schemes of arbitrary complexity, but the intermediate relay nodes are restricted to process only blocks of N symbols. It is well known that for any L and N rarr infin the relays can use a capacity achieving code and communicate reliably as long as the rate of this code is below the capacity of the underlying DMC. The capacity of the cascade is hence equal to the network min-cut capacity. For finite N and L rarr infin, we showed in previous work that the optimal intermediate processing is the highest rate zero-error code of length N for the underlying DMC. The capacity of the cascade coincides with the rate of this zero-error code, and is always below the zero-error capacity. In this work, we characterize how N must scale with L in order to achieve rates in between the zero-error and the min-cut capacity. In particular, we have observed that N = thetas (log L) is sufficient to achieve any rate below the min-cut capacity. Here, we develop a novel upper bound on the capacity of cascades with optimal intermediate processing that applies for any (N, L) pairs and use it to show that N = thetas (log L) is necessary to achieve certain rates above the zero-error capacity. Furthermore, we propose a method to evaluate our upper bound by establishing a connection with the set-cover problem in algorithms

We examine the throughput benefits that network coding offers with respect to the average throughput achievable by routing, where the average throughput refers to the average of the rates that the individual receivers experience. We relate these benefits to the integrality gap of a standard linear programming formulation for the directed Steiner tree problem. We describe families of configurations over which network coding at most doubles the average throughput, and analyze a class of directed graph configurations with N receivers where network coding offers benefits proportional to /spl radic/N. We also discuss other throughput measures in networks, and show how in certain classes of networks, average throughput bounds can be translated into minimum throughput bounds, by employing vector routing and channel coding. Finally, we show configurations where use of randomized coding may require an alphabet size exponentially larger than the minimum alphabet size required.

We propose a method to identify structural properties of multicast network configurations, by decomposing networks into regions through which the same information flows. This decomposition allows us to show that very different networks are equivalent from a coding point of view, and offers a means to identify such equivalence classes. It also allows us to divide the network coding problem into two almost independent tasks: one of graph theory and the other of classical channel coding theory. This approach to network coding enables us to derive the smallest code alphabet size sufficient to code any network configuration with two sources as a function of the number of receivers in the network. But perhaps the most significant strength of our approach concerns future network coding practice. Namely, we propose deterministic algorithms to specify the coding operations at network nodes without the knowledge of the overall network topology. Such decentralized designs facilitate the construction of codes that can easily accommodate future changes in the network, e.g., addition of receivers and loss of links

In this article we propose a set of necessary and sufficient conditions under which the long-term averaged throughput in an ad hoc network can remain constant as the number of nodes n increases. Throughput refers to the minimum achievable rate between a source-destination pair for a given routing mechanism and physical model, when the network is shared by Θ( n ) randomly chosen source-destination pairs. The main idea is to use a connectivity graph , which does not represent the actual physical network but rather the available communication resources. This graph also allows one to translate the problem of maximizing the throughput in ad hoc networks to the multicommodity flow problem and directly apply related results.

We examine the throughput benefits that network coding offers with respect to the average through- put achievable by routing, where the average throughput refers to the average of the rates that the indi- vidual receivers experience. We relate these benefits to the integrality gap of a standard LP formulation for the directed Steiner tree problem. We describe families of configurations over which network coding at most doubles the average throughput, and analyze a class of directed graph configurations with N receivers where network coding offers benefits proportional to √N. We also discuss other throughput measures in networks, and show how in certain classes of networks, the average throughput can be achieved uniformly by all receivers by employing vector routing and channel coding. Finally, we show configurations where use of randomized coding may require an alphabet size exponentially larger than the minimum alphabet size required.

We consider a simple network, where a source and destination node are connected with a line of erasure channels. It is well known that in order to achieve the min-cut capacity, the intermediate nodes are required to process the information. We propose coding schemes for this setting, and discuss each scheme in terms of complexity, delay, achievable rate, memory requirement, and adaptability to unknown channel parameters. We also briefly discuss how these schemes can be extended to more general networks

We consider a source that transmits information to a receiver by routing it over a communication network represented by a graph and examine rate benefits that finite complexity processing at the intermediate nodes may offer. We show that there exist configurations where the optimal rate is achieved only when coding across independent information streams (channel coding and routing cannot be separated); that optimal processing is a function of the particular set of channel parameters and not only of the network topology; and that there exists a connection between linear codes and routing for a special class of graphs

The min-cut, max-flow theorem states that a source node can send a commodity through a network to a sink node at the rate determined by the flow of the min-cut separating the source and the sink. Recently it has been shown that by linear re-encoding at nodes in communication networks, the min-cut rate can be also achieved in multicasting to several sinks. In this paper we discuss connections between such coding schemes and convolutional codes. We propose a method to simplify the convolutional encoder design that is based on a subtree decomposition of the network line graph, describe the structure of the associated matrices, investigate methods to reduce decoding complexity and discuss possible binary implementation.

A subtree decomposition method for network coding is proposed in this paper. This approach enables derivation of tight bounds on the network code alphabet size, makes connections with convolutional codes transparent, allows specification of coding operations at network nodes without the knowledge of the overall network topology, and facilitates design of codes which can easily accommodate future changes in the network, such as addition of receivers and loss of links.

This paper proposes deterministic algorithms for decentralized network coding. Decentralized coding allows us to locally specify the coding operations at network nodes without knowledge of the overall network topology, and to accommodate future changes in the network such as addition of receivers. To the best of our knowledge, these are the first deterministic decentralized algorithms proposed for network coding.

This paper addresses the problem of training sequence design for multiple-antenna transmissions over quasi-static frequency-selective channels. To achieve the channel estimation minimum mean square error, the training sequences transmitted from the multiple antennas must have impulse-like auto correlation and zero cross correlation. We reduce the problem of designing multiple training sequences to the much easier and well-understood problem of designing a single training sequence with impulse-like auto correlation. To this end, we propose to encode the training symbols with a space-time code, that may be the same or different from the space-time code that encodes the information symbols. Optimal sequences do not exist for all training sequence lengths and constellation alphabets. We also propose a method to easily identify training sequences that belong to a standard 2/sup m/-PSK constellation for an arbitrary training sequence length and an arbitrary number of unknown channel taps. Performance bounds derived indicate that these sequences achieve near-optimum performance.

We propose a method to identify training sequences for multiple-antenna transmissions over quasi-static frequency-selective channels. These sequences are constructed to belong to a standard constant-amplitude 2/sup m/-PSK constellation (such as BPSK, QPSK etc) to simplify the transmitter/receiver implementation. Many practical systems use training of predetermined length. Optimal sequences do not exist for all training sequence lengths and constellation alphabets. The proposed method allows us to identify training sequences that belong to a standard constellation for an arbitrary training sequence length and an arbitrary number of unknown channel taps. Performance bounds derived indicate that these sequences achieve near-optimum performance.

The determinant and rank criteria used for space-time code design apply at high SNR. Code design metrics developed for low SNR assume a channel autocorrelation matrix with equal eigenvalues, which does not hold in many practical scenarios. This paper shows that a space-time code designed to ensure full diversity at high SNR can suffer significant degradation when implemented at low-to-medium SNR because of the channel autocorrelation profile. We examine the effect of the channel autocorrelation matrix on a space-time code's performance and discuss how knowledge of this matrix can be used for code design, particularly from the aspect of space-time trellis code minimum memory requirements. Our discussion applies to both flat-fading and frequency-selective channels that are treated in a unified manner.

This paper addresses the problem of training sequence design for multiple-antenna transmissions over quasi-static frequency-selective channels. As performance metric for channel estimation, mean square error is adopted. To achieve the minimum mean square error, the training sequences transmitted from the multiple antennas must have impulse-like autocorrelation and zero crosscorrelation. We reduce the problem of designing multiple training sequences to the much easier and well-understood problem of designing a single training sequence with impulse-like auto-correlation. To this end, we propose to encode the training sequences with a space-time code, that may be the same or different from the space-time code that encodes the information symbols. Designing one instead of multiple training sequences reduces the search space significantly and simplifies the construction of optimal or suboptimal training sequences.

This paper addresses the problem of soft equalization for space-time-coded transmissions over frequency-selective fading channels. The structure of the space-time code is embedded in the channel impulse response for efficient joint equalization and decoding. The proposed equalization/decoding approach uses a prefilter to concentrate the effective channel power in a small number of taps followed by a reduced-complexity maximum a posteriori probability (MAP) equalizer/decoder to produce soft decisions. The prefilter introduces residual intersymbol interference which degrades the performance of MAP when applied to the trellis of the shortened channel. However, the shape of the overall shortened channel impulse response allows the M-algorithm to approximate the prefiltered MAP performance with a small number of states. Based on this general framework, we investigate several enhancements such as using different prefilters for the forward and backward recursions, concatenating two trellis steps during decoding, and temporal oversampling. The performance is evaluated through simulations over the EDGE typical urban channel.

This paper compares bit versus symbol interleaving for parallel-concatenated trellis-coded turbo codes, employing the turbo encoder structure proposed in Benedetto et al., (1996). To compare systems optimized with the same techniques, the paper extends the turbo-encoder design procedure proposed in Fragouli et al. (2001), to bit-interleaved systems. We discuss a method to jointly design the multiple required interleavers for the bit-interleaved system, and a procedure to select constituent encoders that can take advantage of the interleaver structure to achieve a low error floor. Simulation results for the designed bit-interleaved system show better performance than bit-interleaved performance reported in the literature. The symbol-interleaved system though achieves an earlier convergence, especially with an increased number of decoder iterations, but at the cost of a slightly higher error floor.

This paper investigates encoders optimization for the Hamming weight after periodic puncturing, and discusses minimality issues that may affect the performance of the punctured encoders. Periodically puncturing a minimal encoder produces a higher rate encoder that may or may not be minimal. If it is not minimal, it may have a zero-output loop and it may be catastrophic. A code search can use a fast algorithm to determine whether an encoder's state diagram has a zero-output loop under periodic symbol puncturing, and a proposed method to assess the performance of codes with a zero-output loop that are not catastrophic. As an example, the paper optimizes rate-1/4 unpunctured codes for Hamming weight under both bit-wise and symbol-wise periodic puncturing. Code tables and simulation results are included.

This paper presents parallel concatenated turbo codes that employ a non-uniform constellation to achieve shaping gain. The output signal approximates the Gaussian distribution by using equally likely signals with unequal spacing (a non-uniform constellation). The small distance of points near the center of the constellation may lead to a small overall free distance and thus a high error floor for turbo codes. We avoid this situation by a two-step design procedure, that first creates an interleaver, and then identifies the constituent encoders that maximize the turbo code free distance. Simulation results for 4 bits/sec/Hz show that this use of shaping can offer an improvement of approximately 0.2 dB for turbo codes.

This paper addresses turbo-encoder design for coding with high spectral efficiency using parallel concatenated trellis-coded modulation and symbol interleaving. The turbo-encoder design involves the constituent encoder design and the interleaver design. The constituent encoders are optimized for symbol-wise effective free distance, and each has an infinite symbol-wise impulse response. We identify the canonical structures for the constituent encoder search space. In many cases of practical interest, the optimal structure for these constituent encoders connects the memory elements in a single row. This single row generally applies to turbo code constituent encoders for parallel concatenation and is not restricted to symbol interleaving. To lower the error floor, a new semi-random interleaver design criteria and a construction method extends the spread-interleaver concept introduced by Divsalar and Pollara (1995). Simulation results show that the proposed system employing symbol interleaving can converge at a lower signal-to-noise ratio than previously reported systems. We report simulation results between 0.5 and 0.6 db from constrained capacity for rates of 2 and 4 bits/s/Hz.

Abstract The complexity of channel equalization using the BCJR algorithm [Bahl LR et al. IEEE Transactions on Info. Theory 1974; 20: 284–287] grows exponentially with the channel memory. The M‐BCJR algorithm [Franz V, Anderson J. IEEE J. Selected Areas Comm. 1998; 16(2): 186–195] provides a method for reduced‐trellis channel equalization, but its performance varies significantly with the distribution of a channel energy to its taps. This paper proposes a variation of the M‐algorithm, based on the implementation of the BCJR algorithm in the logarithmic domain, which can offer robust performance. Designer choices such as the decision delay, maximum and minimum phase transformation, and selection of states are discussed. Simulation results demonstrate the effect of different parameters on the proposed algorithm's performance. Copyright © 2001 John Wiley & Sons, Ltd.

This paper addresses the problem of adaptive channel tracking and equalization for multi-input multi-output (MIMO) time-variant frequency-selective channels. A finite-length minimum-mean-squared-error decision-feedback equalizer (MMSE-DFE) performs the equalization task, while a Kalman filter tracks the MIMO channel, which models the corrupting effects of inter-symbol interference (ISI), inter-user interference (IUI), and noise. The Kalman tracking is aided by previous hard decisions produced by the DFE, with a decision delay /spl Delta/>0, which causes the Kalman filter to track the channel with a delay. A channel prediction module bridges the time gap between the channel estimates produced by the Kalman filter and those needed for the DFE adaptation. The proposed algorithm offers good tracking behavior for multi-user fading ISI channels at the expense of higher complexity.

A key problem in transporting multimedia traffic across wireless networks is a controlled sharing of the wireless link by different packet streams. So far this problem has been treated as that of providing support for quality of service in time division multiplexing based medium access control protocols (MAC). Adopting a different perspective to the problem, this paper describes an approach based on extending the class-based queueing (CBQ) based controlled hierarchical link sharing model proposed for the Internet. Our scheme enhances CBQ, which works well in wired links such as point-to-point wires of fixed bandwidth, to also work well with wireless links based on radio channels that are (i) inherently shared on-demand among multiple radios, and (ii) are subject to highly dynamic bandwidth variations due to spatially and temporally varying fading with accompanying burst errors. The proposed scheme is based on combining a modified version of CBQ with channel-state dependent packet scheduling.

Energy efficiency, which directly affects battery life and portability, is perhaps the single most important design metric in hand-held computing devices capable of mobile networking over wireless radio links.By virtue of their being relatively thin clients, a high fraction of the power consumption in portable wireless computing devices is accounted for by the transport of packet data over the wireless link [Stemm96].In particular, the error con-.trol strategy (e.g.convolutional and block channel coding for forward error correction (FBC), ARQ protocols, hybrids) used for wireless link data transport has a direct impact on battery power consumption.Error control has traditionally been studied by channel coding researchers from the perspective of selecting an error control scheme to achieve a desired level of radio channel performance.We instead study the problem of error control from a perspective more relevant to battery operated devices: the amount of battery energy consumed to transmit bits across a wireless link.This includes both the physical transmission of useful and redundancy data, as well as the computation of the error control redundancy.We first describe a novel error control where the most battery energy efficient hybrid combination of an appropriate FBC code and ABQ protocol is chosen, and adapted over time, for each stream (ATM virtual circuit or IP/RSVP flow).Next, we present analysis and simulation results to guide the selection and adaptation of the most energy efficient error control scheme as a function of quality of service, packet size, and channel state.