arXiv subjects

Asaf Cohen

Publications and source records attributed to Asaf Cohen.

At least 91 records · Page 5Linked to original sources

arXiv2016

Maximum Entropy Functions: Approximate Gacs-Korner for Distributed Compression

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

cs.IT↗

arXiv2016

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

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

cs.IT↗

arXiv2015

Coded Retransmission in Wireless Networks Via Abstract MDPs: Theory and Algorithms

Consider a transmission scheme with a single transmitter and multiple receivers over a faulty broadcast channel. For each receiver, the transmitter has a unique infinite stream of packets, and its goal is to deliver them at the highest throughput possible. While such multiple-unicast models are unsolved in general, several network coding based schemes were suggested. In such schemes, the transmitter can either send an uncoded packet, or a coded packet which is a function of a few packets. The packets sent can be received by the designated receiver (with some probability) or heard and stored by other receivers. Two functional modes are considered; the first presumes that the storage time is unlimited, while in the second it is limited by a given Time to Expire (TTE) parameter. We model the transmission process as an infinite-horizon Markov Decision Process (MDP). Since the large state space renders exact solutions computationally impractical, we introduce policy restricted and induced MDPs with significantly reduced state space, and prove that with proper reward function they have equal optimal value function (hence equal optimal throughput). We then derive a reinforcement learning algorithm, which learns the optimal policy for the induced MDP. This optimal strategy of the induced MDP, once applied to the policy restricted one, significantly improves over uncoded schemes. Next, we enhance the algorithm by means of analysis of the structural properties of the resulting reward functional. We demonstrate that our method scales well in the number of users, and automatically adapts to the packet loss rates, unknown in advance. In addition, the performance is compared to the recent bound by Wang, which assumes much stronger coding (e.g., intra-session and buffering of coded packets), yet is shown to be comparable.

cs.IT↗

arXiv2015

Minimizing Lifetime Poverty with a Penalty for Bankruptcy

We provide investment advice for an individual who wishes to minimize her lifetime poverty, with a penalty for bankruptcy or ruin. We measure poverty via a non-negative, non-increasing function of (running) wealth. Thus, the lower wealth falls and the longer wealth stays low, the greater the penalty. This paper generalizes the problems of minimizing the probability of lifetime ruin and minimizing expected lifetime occupation, with the poverty function serving as a bridge between the two. To illustrate our model, we compute the optimal investment strategies for a specific poverty function and two consumption functions, and we prove some interesting properties of those investment strategies.

q-fin.PM↗

arXiv2015

Universal Anomaly Detection: Algorithms and Applications

Modern computer threats are far more complicated than those seen in the past. They are constantly evolving, altering their appearance, perpetually changing disguise. Under such circumstances, detecting known threats, a fortiori zero-day attacks, requires new tools, which are able to capture the essence of their behavior, rather than some fixed signatures. In this work, we propose novel universal anomaly detection algorithms, which are able to learn the normal behavior of systems and alert for abnormalities, without any prior knowledge on the system model, nor any knowledge on the characteristics of the attack. The suggested method utilizes the Lempel-Ziv universal compression algorithm in order to optimally give probability assignments for normal behavior (during learning), then estimate the likelihood of new data (during operation) and classify it accordingly. The suggested technique is generic, and can be applied to different scenarios. Indeed, we apply it to key problems in computer security. The first is detecting Botnets Command and Control (C&C) channels. A Botnet is a logical network of compromised machines which are remotely controlled by an attacker using a C&C infrastructure, in order to perform malicious activities. We derive a detection algorithm based on timing data, which can be collected without deep inspection, from open as well as encrypted flows. We evaluate the algorithm on real-world network traces, showing how a universal, low complexity C&C identification system can be built, with high detection rates and low false-alarm probabilities. Further applications include malicious tools detection via system calls monitoring and data leakage identification.

cs.CR↗

arXiv2015

Capacity and performance analysis for multi-user system under distributed opportunistic scheduling in a time dependent channel

Consider the problem of a multi-user multiple access channel. While several multi-user coding techniques exist, in practical scenarios, not all users can be scheduled simultaneously. Thus, a key problem is which users to schedule in a given time slot. Under realistic approach for time dependency of the channel, we adopt a distributed scheduling algorithm in which each user, in the beginning of each slot, estimates his channel gain and compares it to a threshold, and if exceeding it the user can transmit. In this work we are interested in the expected capacity of the system and the delay and quality of service of the data accumulated at the users under this scheduling scheme. First we derive the expected capacity under scheduling (distributed and centralized) for this time dependent environment and show that its scaling law is $O(σ_g\sqrt{2\log K}+μ_g)$, were $σ_g, μ_g$ are the good channel parameters (assuming Gaussian capacity approximation, e.g., under MIMO) and $K$ is the number of users. Then we turn to the performance analysis of such system while assuming the users are not necessarily fully backlogged, and focus specifically on the queueing problem and the strong dependence between the queues which leave no alternative but to turn to approximate models for this system. We adopt the celebrated model of Ephremides and Zhu to give new results on the convergence of the probability of collision to its average value (as the number of users grows), and hence for the ensuing system performance metrics, such as throughput and delay. We further utilize this finding to suggest a much simpler approximate model, which accurately describes the system behavior when the number of queues is large. The system performance as predicted by the approximate models shows excellent agreement with simulation results.

cs.IT↗

arXiv2015

Asymptotic Analysis for Reliable Data Dissemination in Shared loss Multicast Trees

The completion time for the dissemination (or alternatively, aggregation) of information from all nodes in a network plays a critical role in the design and analysis of communication systems, especially in real time applications for which delay is critical. In this work, we analyse the completion time of data dissemination in a shared loss (i.e., unreliable links) multicast tree, at the limit of large number of nodes. Specifically, analytic expressions for upper and lower bounds on the expected completion time are provided, and, in particular, it is shown that both these bounds scale as $α\log n$. For example, on a full binary tree with $n$ end users, and packet loss probability of $0.1$, we bound the expected completion time for disseminating one packet from below by $1.41 \log_2 n+o \left( \log n \right)$ and from above by $1.78 \log_2 n+o \left( \log n \right)$. Clearly, the completion time is determined by the last end user who receives the message, that is, a maximum over all arrival times. Hence, Extreme Value Theory (EVT) is an appropriate tool to explore this problem. However, since arrival times are correlated, non-stationary, and furthermore, time slots are discrete, a thorough study of EVT for Non-Stationary Integer Valued (NSIV) sequences is required. To the best of our knowledge, such processes were not studied before in the framework of EVT. Consequently, we derive the asymptotic distribution of the maxima of NSIV sequences satisfying certain conditions, and give EVT results which are applicable also beyond the scope of this work. These result are then used to derive tight bounds on the completion time. Finally, the results are validated by extensive simulations and numerical analysis.

cs.NI↗

arXiv2015

On the Capacity of Wireless Networks with Random Transmission Delay

In this paper, we introduce novel coding schemes for wireless networks with random transmission delays. These coding schemes obviate the need for synchronicity, reduce the number of transmissions and achieve the optimal rate region in the corresponding wired model for both multiple unicast and multicast cases with up to three users under the equal rate constraint. The coding schemes are presented in two phases; first, coding schemes for line, star and line-star topologies with random transmission delays are provided. Second, any general topology with multiple bidirectional unicast and multicast sessions is shown to be decomposable into these canonical topologies to reduce the number of transmissions without rate redundancy. As a result, the coding schemes developed for the line, star and line-star topologies serve as building blocks for the construction of more general coding schemes for all networks. The proposed schemes are proved to be Real Time (RT) for wireless networks in the sense that they achieve the minimal decoding delay. With a negligible size header, these coding schemes are shown to be applicable to unsynchronized networks, i.e., networks with random transmission delays. Finally, we demonstrate the applicability of these schemes by extensive simulations. The implementation of such coding schemes on a wireless network with random transmission delay can improve performance and power efficiency.

cs.IT↗

arXiv2014

A differential game for a multiclass queueing model in the moderate-deviation heavy-traffic regime

We study a differential game that governs the moderate-deviation heavy-traffic asymptotics of a multiclass single-server queueing control problem with a risk-sensitive cost. We consider a cost set on a finite but sufficiently large time horizon, and show that this formulation leads to stationary feedback policies for the game. Several aspects of the game are explored, including its characterization via a (one-dimensional) free boundary problem, the semi-explicit solution of an optimal strategy, and the specification of a saddle point. We emphasize the analogy to the well-known Harrison-Taksar free boundary problem which plays a similar role in the diffusion-scale heavy-traffic literature.

math.PR↗

arXiv2014

Wiretap Channel With Causal State Information and Secure Rate-Limited Feedback

In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf . We shown that the secrecy capacity is bounded. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving scheme is based on both the Wyner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. Finally, we consider several special cases. When state information is available only at the legitimate receiver, the analysis suggests that unlike previous results involving feedback, it is better to use the feedback to send the state information to the transmitter (when possible), rather than send a random key.

cs.IT↗

arXiv2014

Parameter Estimation: The Proper Way to Use Bayesian Posterior Processes with Brownian Noise

This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior distribution processes is, in general, not equal to the posterior distribution process of the mentioned Brownian motion with the unknown drift. Instead, it is equal to the posterior distribution process associated with a Brownian motion with the same unknown drift and a different standard deviation coefficient. The difference between the two standard deviation coefficients can be arbitrarily large. The characterization of the limit of the posterior distribution processes is then applied to a family of stopping time problems. We show that the proper way to find asymptotically optimal solutions to stopping time problems w.r.t.~the scaled counting processes is by looking at the limit of the posterior distribution processes rather than by the naive approach of looking at the limit of the scaled counting processes themselves. The difference between the performances can be arbitrarily large.

math.ST↗

arXiv2014

Bandit problems with Levy processes

Bandit problems model the trade-off between exploration and exploitation in various decision problems. We study two-armed bandit problems in continuous time, where the risky arm can have two types: High or Low; both types yield stochastic payoffs generated by a Levy process. We show that the optimal strategy is a cut-off strategy and we provide an explicit expression for the cut-off and for the optimal payoff.

math.PR↗

arXiv2014

Lossless Coding of Correlated Sources with Actions

This work studies the problem of distributed compression of correlated sources with an action-dependent joint distribution. This class of problems is, in fact, an extension of the Slepian-Wolf model, but where cost-constrained actions taken by the encoder or the decoder affect the generation of one of the sources. The purpose of this work is to study the implications of actions on the achievable rates. In particular, two cases where transmission occurs over a rate-limited link are studied; case A for actions taken at the decoder and case B where actions are taken at the encoder. A complete single-letter characterization of the set of achievable rates is given in both cases. Furthermore, a network coding setup is investigated for the case where actions are taken at the encoder. The sources are generated at different nodes of the network and are required at a set of terminal nodes, yet transmission occurs over a general, acyclic, directed network. For this setup, generalized cut-set bounds are derived, and a full characterization of the set of achievable rates using single-letter expressions is provided. For this scenario, random linear network coding is proved to be optimal, even though this is not a classical multicast problem. Additionally, two binary examples are investigated and demonstrate how actions taken at different nodes of the system have a significant affect on the achievable rate region in comparison to a naive time-sharing strategy.

cs.IT↗

arXiv2013

SINR Diagram with Interference Cancellation

In this paper we study the reception zones of a wireless network in the SINR model with receivers that employ \emph{interference cancellation} (IC), a technique that allows a receiver to decode interfering signals, and \emph{cancel} them from the received signal in order to decode its intended message. We first derive some important topological properties of the diagram describing the reception zones and their connections to \emph{high-order Voronoi diagrams} and other related geometric objects. We then discuss the computational issues that arise when seeking an efficient description of the zones. Our main fundamental result states that although potentially there are exponentially many possible cancellation orderings (and consequently reception cells), in fact there are much fewer nonempty such cells. We prove a (tight) linear bound on the number of cells and provide a polynomial time algorithm to describe the diagram. Moreover, we introduce a novel measure, referred to as the \emph{Compactness Parameter}, which influences the tightness of our bounds. We then utilize the properties established for reception diagrams to devise a logarithmic time algorithm for answering \emph{point-location} queries for networks with IC.

cs.CG↗

arXiv2013

Distributed Inter-Cell Interference Mitigation Via Joint Scheduling and Power Control Under Noise Rise Constraints

Consider the problem of joint uplink scheduling and power allocation. Being inherent to almost any wireless system, this resource allocation problem has received extensive attention. Yet, most common techniques either adopt classical power control, in which mobile stations are received with the same Signal-to-Interference-plus-Noise Ratio, or use centralized schemes, in which base stations coordinate their allocations. In this work, we suggest a novel scheduling approach in which each base station, besides allocating the time and frequency according to given constraints, also manages its uplink power budget such that the aggregate interference, "Noise Rise", caused by its subscribers at the neighboring cells is bounded. Our suggested scheme is distributed, requiring neither coordination nor message exchange. We rigorously define the allocation problem under noise rise constraints, give the optimal solution and derive an efficient iterative algorithm to achieve it. We then discuss a relaxed problem, where the noise rise is constrained separately for each sub-channel or resource unit. While sub-optimal, this view renders the scheduling and power allocation problems separate, yielding an even simpler and more efficient solution, while the essence of the scheme is kept. Via extensive simulations, we show that the suggested approach increases overall performance dramatically, with the same level of fairness and power consumption.

cs.NI↗

arXiv2012

Opportunistic Scheduling in Heterogeneous Networks: Distributed Algorithms and System Capacity

In this work, we design and analyze novel distributed scheduling algorithms for multi-user MIMO systems. In particular, we consider algorithms which do not require sending channel state information to a central processing unit, nor do they require communication between the users themselves, yet, we prove their performance closely approximates that of a centrally-controlled system, which is able to schedule the strongest user in each time-slot. Our analysis is based on a novel application of the Point-Process approximation. This novel technique allows us to examine non-homogeneous cases, such as non-identically distributed users, or handling various QoS considerations, and give exact expressions for the capacity of the system under these schemes, solving analytically problems which to date had been open. Possible application include, but are not limited to, modern 4G networks such as 3GPP LTE, or random access protocols.

cs.IT↗

arXiv2012

Network Coded Gossip with Correlated Data

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

cs.IT↗

arXiv2012

Sensor Networks: from Dependence Analysis Via Matroid Bases to Online Synthesis

Consider the two related problems of sensor selection and sensor fusion. In the first, given a set of sensors, one wishes to identify a subset of the sensors, which while small in size, captures the essence of the data gathered by the sensors. In the second, one wishes to construct a fused sensor, which utilizes the data from the sensors (possibly after discarding dependent ones) in order to create a single sensor which is more reliable than each of the individual ones. In this work, we rigorously define the dependence among sensors in terms of joint empirical measures and incremental parsing. We show that these measures adhere to a polymatroid structure, which in turn facilitates the application of efficient algorithms for sensor selection. We suggest both a random and a greedy algorithm for sensor selection. Given an independent set, we then turn to the fusion problem, and suggest a novel variant of the exponential weighting algorithm. In the suggested algorithm, one competes against an augmented set of sensors, which allows it to converge to the best fused sensor in a family of sensors, without having any prior data on the sensors' performance.

cs.IT↗