arXiv subjects

Omer Gurewitz

Publications and source records attributed to Omer Gurewitz.

At least 19 recordsLinked to original sources

arXiv2026

On Cost-Aware Designs for Sequential Hypothesis Testing

We introduce Cost-Aware (CA) Sequential Hypothesis Testing (CASHT), in which an active decision-maker selects sensing actions with differing, random costs to identify the true hypothesis under an average-error constraint $δ$ while minimizing the expected total cost rather than the number of samples. For fixed costs, we prove that the optimal expected total cost scales as $Θ(\log(1/δ))$, and is achievable by Multihypothesis Sequential Probability Ratio Test-based procedures. We show that the CA design principle is to maximize the ratio of expected information gain to expected cost under the policy-induced action distribution. Guided by this principle, we adapt two classic policies to the CA setting and establish their asymptotic optimality. We then treat random costs under two revelation models: ex-post, where costs are disclosed only after a sample is obtained, and the cost-error tradeoff coincides with the fixed-cost case, and ex-ante, where costs accrue before acquisition, and the decision maker may cancel an action mid-operation. For the ex-ante model, we characterize when cancellation lowers the total cost and analyze several cost distributions in detail. Simulations confirm our findings that the CA variants consistently reduce total cost relative to their classical counterparts, and when action cancellation helps or hurts.

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arXiv2026

Iterative Hypothesis Pruning and Distribution-based Early Labeling for Sequential Hypothesis Testing

We consider the framework of Sequential Hypothesis Testing (SHT), in which a decision maker (DM) selects actions that generate samples from known, action-dependent distributions, while the realized distribution is determined by an unknown true hypothesis. To identify this hypothesis, we adopt the elimination perspective and propose three deterministic, adaptive, multi-iteration algorithms with a common structure, termed $Φ$, $Φ$-$Δ$, and $I$. In each iteration, the DM selects an action and repeatedly applies it to collect samples, after which hypotheses inconsistent with the observed data are eliminated. The algorithms differ in the criterion used to terminate each iteration: $Φ$ continues until one hypothesis dominates all others; $Φ$-$Δ$ first clusters hypotheses whose per-action distributions are close in total variation and then proceeds in the spirit of $Φ$; $I$ continues until one hypothesis can be safely discarded. We analyze our algorithms, establishing: (i) controlled error-rates, (ii) controlled sample complexity, (iii) asymptotic optimality, (iv) computational complexity, and (v) NP-hardness of the optimal action-sequence selection for minimal sample complexity.

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arXiv2025

Active Sequential Hypothesis Testing with Non-Homogeneous Costs

We study the Non-Homogeneous Sequential Hypothesis Testing (NHSHT), where a single active Decision-Maker (DM) selects actions with heterogeneous positive costs to identify the true hypothesis under an average error constraint $δ$, while minimizing expected total cost paid. Under standard arguments, we show that the objective decomposes into the product of the mean number of samples and the mean per-action cost induced by the policy. This leads to a key design principle: one should optimize the ratio of expectations (expected information gain per expected cost) rather than the expectation of per-step information-per-cost ("bit-per-buck"), which can be suboptimal. We adapt the Chernoff scheme to NHSHT, preserving its classical $\log 1/δ$ scaling. In simulations, the adapted scheme reduces mean cost by up to 50\% relative to the classic Chernoff policy and by up to 90\% relative to the naive bit-per-buck heuristic.

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arXiv2025

Multi-Stage Active Sequential Hypothesis Testing with Clustered Hypotheses

We consider the problem where an active Decision-Maker (DM) is tasked to identify the true hypothesis using as few as possible observations while maintaining accuracy. The DM collects observations according to its determined actions and knows the distributions under each hypothesis. We propose a deterministic and adaptive multi-stage hypothesis-elimination strategy where the DM selects an action, applies it repeatedly, and discards hypotheses in light of its obtained observations. The DM selects actions based on maximal separation expressed by the distance between the parameter vectors of each distribution under each hypothesis. Close distributions can be clustered, simplifying the search and significantly reducing the number of required observations. Our algorithms achieve vanishing Average Bayes Risk (ABR) as the error probability approaches zero, i.e., the algorithm is asymptotically optimal. Furthermore, we show that the ABR is bounded when the number of hypotheses grows. Simulations are carried out to evaluate the algorithm's performance compared to another multi-stage hypothesis-elimination algorithm, where an improvement of several orders of magnitude in the mean number of observations required is observed.

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arXiv2023

Order-optimal Joint Transmission and Identification in Massive Multi-User MIMO via Group Testing

The number of wireless devices which are connected to a single Wireless Local Area Network continues to grow each year. As a result, the orchestration of so many devices becomes a daunting, resource--consuming task, especially when the resources available at the single access point are limited, and it is hard to anticipate which devices will request access at any given time. On the other hand, the number of antennas on both the devices and the access point grows as well, facilitating advanced joint scheduling and coding techniques. In this paper, we leverage the large number of antennas and suggest a massive multiple-user multiple-input-multiple-output (MU-MIMO) scheme using sparse coding based on Group Testing (GT) principles. The scheme allows for a small subset of devices to transmit simultaneously, without a preceding scheduling phase or coordination, thus reducing overhead and complexity. Specifically, we show that out of a population of $N$ devices, it is possible to jointly identify and decode $K$ devices, unknown in advance, simultaneously and without any scheduling. The scheme utilizes minimal knowledge of channel state, uses an efficient (in both run-time and space) decoding algorithm, and requires $O(K\log N\mathcal{M})$ antennas, where $\mathcal{M}$ is the number of messages per device. In fact, we prove that this scheme is order--optimal in the number of users and messages. This is done by deriving sufficient conditions for a vanishing error probability (a direct result), bounding the minimal number of antennas necessary for any such scheme (a converse result), and showing that these results are asymptotically tight.

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arXiv2021

Secure Multi-Source Multicast

The principal mission of Multi-Source Multicast (MSM) is to disseminate all messages from all sources in a network to all destinations. MSM is utilized in numerous applications. In many of them, securing the messages disseminated is critical. A common secure model is to consider a network where there is an eavesdropper which is able to observe a subset of the network links, and seek a code which keeps the eavesdropper ignorant regarding all the messages. While this is solved when all messages are located at a single source, Secure MSM (SMSM) is an open problem, and the rates required are hard to characterize in general. In this paper, we consider Individual Security, which promises that the eavesdropper has zero mutual information with each message individually. We completely characterize the rate region for SMSM under individual security, and show that such a security level is achievable at the full capacity of the network, that is, the cut-set bound is the matching converse, similar to non-secure MSM. Moreover, we show that the field size is similar to non-secure MSM and does not have to be larger due to the security constraint.

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arXiv2020

Secure Adaptive Group Testing

\emph{Group Testing} (GT) addresses the problem of identifying a small subset of defective items from a large population, by grouping items into as few test pools as possible. In \emph{Adaptive GT} (AGT), outcomes of previous tests can influence the makeup of future tests. Using an information theoretic point of view, Aldridge $2012$ showed that in the regime of a few defectives, adaptivity does not help much, as the number of tests required is essentially the same as for non-adaptive GT. \emph{Secure GT} considers a scenario where there is an eavesdropper who may observe a fraction $δ$ of the tests results, yet should not be able to infer the status of the items. In the non-adaptive scenario, the number of tests required is $1/(1-δ)$ times the number of tests without the secrecy constraint. In this paper, we consider \emph{Secure Adaptive GT}. Specifically, when during the makeup of the pools one has access to a private feedback link from the lab, of rate $R_f$. We prove that the number of tests required for both correct reconstruction at the legitimate lab, with high probability, and negligible mutual information at the eavesdropper is $1/min\{1,1-δ+R_f\}$ times the number of tests required with no secrecy constraint. Thus, unlike non-secure GT, where an adaptive algorithm has only a mild impact, under a security constraint it can significantly boost performance. A key insight is that not only the adaptive link should disregard the actual test results and simply send keys, these keys should be enhanced through a "secret sharing" scheme before usage. We drive sufficiency and necessity bounds that completely characterizes the Secure Adaptive GT capacity.

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arXiv2020

Secure Group Testing

The principal goal of Group Testing (GT) is to identify a small subset of "defective" items from a large population, by grouping items into as few test pools as possible. The test outcome of a pool is positive if it contains at least one defective item, and is negative otherwise. GT algorithms are utilized in numerous applications, and in many of them maintaining the privacy of the tested items, namely, keeping secret whether they are defective or not, is critical. In this paper, we consider a scenario where there is an eavesdropper (Eve) who is able to observe a subset of the GT outcomes (pools). We propose a new non-adaptive Secure Group Testing (SGT) scheme based on information-theoretic principles. The new proposed test design keeps the eavesdropper ignorant regarding the items' status. Specifically, when the fraction of tests observed by Eve is $0 \leq δ<1$, we prove that with the naive Maximum Likelihood (ML) decoding algorithm the number of tests required for both correct reconstruction at the legitimate user (with high probability) and negligible information leakage to Eve is $\frac{1}{1-δ}$ times the number of tests required with no secrecy constraint for the fixed $K$ regime. By a matching converse, we completely characterize the Secure GT capacity. Moreover, we consider the Definitely Non-Defective (DND) computationally efficient decoding algorithm, proposed in the literature for non-secure GT. We prove that with the new secure test design, for $δ< 1/2$, the number of tests required, without any constraint on $K$, is at most $\frac{1}{1/2-δ}$ times the number of tests required with no secrecy constraint.

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arXiv2020

Multi-Antenna Jamming in Covert Communication

Covert communication conceals transmission of messages from Alice to Bob out of a watchful adversary, Willie, who tries to determine if a transmission took place or not. While covert communication in a basic, vanilla setting where all variables are known to Willie, results in the well-known square-root law, when a jammer is present and assists Alice by creating uncertainty in Willie's decoder, a strictly positive transmission rate is possible. In this work, we analyze the case where the jammer is equipped with multiple antennas. Specifically, we analyze the effect of multiple antennas at the jammer on Alice's transmission power and consequently on the transmission rate. We consider both cases, one in which the channel knowledge is known and one in which it is unknown by the jammer. We formulate several optimization problems for the transmission strategies of the jammer, to maximize his assistance to Alice, in terms of maximizing a ratio between Willie's and Bob's noise variances. When the channel information is known to the jammer, we show that the optimal strategy of the jammer is to perform beamforming towards a single direction with all his available power. This direction though, is not trivial, since it reflects an optimal tradeoff point between minimizing the interference at Bob and maximizing the interference at Willie. When the channel knowledge is unknown, we show that the optimal strategy of the jammer is either to transmit isotropically to all directions or to the null-space of Bob, where this choice depends on certain channel conditions. This is in contrast to current schemes in the literature. Furthermore, we extend the optimization problems to the case where Bob is also equipped with multiple antennas, and provide insightful results, shown to be asymptotically optimal, accompanied by simulations.

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arXiv2020

Compute-and-Forward in Large Relaying Systems: Limitations and Asymptotically Optimal Scheduling

Compute and Forward (CF) is a coding scheme which enables receivers to decode linear combinations of simultaneously transmitted messages while exploiting the linear properties of lattice codes and the additive nature of a shared medium. The scheme was originally designed for relay networks, yet, it was found useful in other communication problems, such as MIMO communication. Works in the current literature assume a fixed number of transmitters and receivers in the system. However, following the increase in communication networks density, it is interesting to investigate the performance of CF when the number of transmitters is large. In this work, we show that as the number of transmitters grows, CF becomes degenerated, in the sense that a relay prefers to decode only one (strongest) user instead of any other linear combination of the transmitted codewords, treating the other users as noise. Moreover, the system's sum-rate tends to zero as well. This makes scheduling necessary in order to maintain the superior abilities CF provides. We thus examine the problem of scheduling for CF. We start with insights on why good scheduling opportunities can be found. Then, we provide an asymptotically optimal, polynomial-time scheduling algorithm and analyze its performance. We conclude that with proper scheduling, CF is not merely non-degenerated, but, in fact, provides a gain for the system sum-rate, up to the optimal scaling law of $O(\log{\log{L}})$.

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arXiv2019

VM Scaling and Load Balancing via Cost Optimal MDP Solution

We address a cost optimization problem faced by a user who runs instances of applications in a remote cloud configuration constructed of multiple virtual machines (VMs). Each VM runs a single application instance which can execute tasks specific to that application. Managing the VMs involves a sophisticated trade-off between cloud-related demands, which are expressed by the provisional costs of leased cloud resources, and exogenous cost demands expressed by service revenues that are typically bound to SLAs. The internal costs may include VM deployment/termination cost, and VM lease cost. The exogenous costs refer to rewards accumulated due to the successfully accomplished tasks being run by each application instance. In the case where the SLA restricts performance to a certain load level at each VM, tasks incoming at VMs that reached that level are rejected. Rejections cause fines deducted against the rewards. The performance level is also quantified, namely, by means of a delay cost, according to the average delay experienced by tasks. Typical examples for specific applications which fall within this class of problems include handling of scientific worklflows and network functioning virtualization (NFV). We model this problem by cost-optimal load balancing to a queuing system with a flexible number of queues, where a queue (VM) can be deployed, can have a task directed to it and can be terminated. We analyze the system by Markov decision process (MDP) and numerically solve it to find the optimal policy, which captures the aforementioned costs and performance constraints. Within this constrained framework, we also investigate the impact of average VM deployment time. We show that the optimal policy possesses decision thresholds which depend on several parameters. We validate policies found by MDP, through directing an exogenous computational tasks flow to a set-up implemented on AWS.

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arXiv2018

Asymptotically Optimal Scheduling for Compute-and-Forward

Consider a Compute and Forward (CF) relay network with $L$ users and a single relay. The relay tries to decode a linear function of the transmitted signals. For such a network, letting all $L$ users transmit simultaneously, especially when $L$ is large, causes a significant degradation in the rate in which the relay is able to decode. In fact, the rate goes to zero very fast with $L$. Therefore, in each transmission phase only a fixed number of users should transmit, i.e., users should be scheduled. In this work, we examine the problem of scheduling for CF and lay the foundations for identifying the optimal schedule which, to date, lacks a clear understanding. Specifically, we start with insights why when the number of users is large, good scheduling opportunities can be found. Then, we provide an asymptotically optimal, polynomial time scheduling algorithm and analyze it's performance. We conclude that scheduling under CF provides a gain in the system sum-rate, up to the optimal scaling law of $O(\log{\log{L}})$.

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arXiv2018

Efficient Data Collection Over Multiple Access Wireless Sensors Network

Data collection in Wireless Sensor Networks (WSN) draws significant attention, due to emerging interest in technologies raging from Internet of Things (IoT) networks to simple "Presence" applications, which identify the status of the devices (active or inactive). Numerous Medium Access Control (MAC) protocols for WSN, which can address the challenge of data collection in dense networks, were suggested over the years. Most of these protocols utilize the traditional layering approach, in which the MAC layer is unaware of the encapsulated packet payload, and therefore there is no connection between the data collected, the physical layer and the signaling mechanisms. Nonetheless, in many of the applications that intend to utilize such protocols, nodes may need to exchange very little information, and do so only sporadically, that is, while the number of devices in the network can be very large, only a subset wishes to transmit at any given time. Thus, a tailored protocol, which matches the signaling, physical layer and access control to traffic patterns is required. In this work, we design and analyze a data collection protocol based on information theoretic principles. In the suggested protocol, the sink collects messages from up to K sensors simultaneously, out of a large population of sensors, without knowing in advance which sensors will transmit, and without requiring any synchronization, coordination or management overhead. In other words, neither the sink nor the other sensors need to know who are the actively transmitting sensors, and this data is decoded directly from the channel output. We provide a simple codebook construction with very simple encoding and decoding procedures. We further design a secure version of the protocol.

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arXiv2018

The Ergodic Capacity of the Multiple Access Channel Under Distributed Scheduling - Order Optimality of Linear Receivers

Consider the problem of a Multiple-Input Multiple-Output (MIMO) Multiple-Access Channel (MAC) at the limit of large number of users. Clearly, in practical scenarios, only a small subset of the users can be scheduled to utilize the channel simultaneously. Thus, a problem of user selection arises. However, since solutions which collect Channel State Information (CSI) from all users and decide on the best subset to transmit in each slot do not scale when the number of users is large, distributed algorithms for user selection are advantageous. In this paper, we analyse a distributed user selection algorithm, which selects a group of users to transmit without coordinating between users and without all users sending CSI to the base station. This threshold-based algorithm is analysed for both Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) receivers, and its expected sum-rate in the limit of large number of users is investigated. It is shown that for large number of users it achieves the same scaling laws as the optimal centralized scheme.

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arXiv2017

Integer Forcing: Effective SNR Distribution and Practical Block-Based Schemes

Integer Forcing (IF) is a novel linear receiver architecture, where instead of separating the codewords sent by each transmitter, and decoding them individually, forces integer-valued linear combinations at each receive antenna, and decodes the linear combinations. The original codewords are obtained by inverting the integer-valued matrix. While demonstrating superior performance, IF requires complex optimization in order to find the optimal linear combinations, and demands either using multi-level nested lattice codes, or reducing the rates of all transmitters to equal the weakest one. Finally, the distribution of the resulting effective SNR is hard to evaluate. In this paper, we first give simple upper and lower bounds on the effective SNR of a single linear combination in IF. These expressions allow us to easily bound the distribution of the effective SNR for any given linear combination used. We then suggest two simple block-based IF schemes. These schemes, while sub-optimal, significantly reduce the complexity of the optimization process, and, more importantly, do not require reducing the rates of all transmitters, as decoding is done block-wise. Finally, we bound the distribution of the effective SNR of the decoding schemes, and show via simulations the superiority of block-wise schemes at low SNR.

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arXiv2017

Distributed Scheduling in Time Dependent Environments: Algorithms and Analysis

Consider the problem of a multiple access channel in a time dependent environment with a large number of users. In such a system, mostly due to practical constraints (e.g., decoding complexity), not all users can be scheduled together, and usually only one user may transmit at any given time. Assuming a distributed, opportunistic scheduling algorithm, we analyse the system's properties, such as delay, QoS and capacity scaling laws. Specifically, we start with analyzing the performance while \emph{assuming the users are not necessarily fully backlogged}, focusing on the queueing problem and, especially, on the \emph{strong dependence between the queues}. We first extend a known queueing model by 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. This model, however, is limited in the number of users one can analyze. We thus suggest a new model, which is much simpler yet can accurately describes the system behaviour when the number of users is large. We then proceed to the analysis of this system under the assumption of time dependent channels. Specifically, we assume each user experiences a different channel state sequence, expressing different channel fluctuations (specifically, the Gilbert-Elliott model). The system performance under this setting is analysed, along with the channel capacity scaling laws.

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arXiv2017

The Necessity of Scheduling in Compute-and-Forward

Compute and Forward (CF) is a promising relaying scheme which, instead of decoding single messages or forwarding/amplifying information at the relay, decodes linear combinations of the simultaneously transmitted messages. The current literature includes several coding schemes and results on the degrees of freedom in CF, yet for systems with a fixed number of transmitters and receivers. It is unclear, however, how CF behaves at the limit of a large number of transmitters. In this paper, we investigate the performance of CF in that regime. Specifically, we show that as the number of transmitters grows, CF becomes degenerated, in the sense that a relay prefers to decode only one (strongest) user instead of any other linear combination of the transmitted codewords, treating the other users as noise. Moreover, the sum-rate tends to zero as well. This makes scheduling necessary in order to maintain the superior abilities CF provides. Indeed, under scheduling, we show that non-trivial linear combinations are chosen, and the sum-rate does not decay, even without state information at the transmitters and without interference alignment.

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arXiv2017

Optimal Dynamic Routing for the Wireless Relay Channel

Consider a communication network with a source, a relay and a destination. Each time interval, the source may dynamically choose between a few possible coding schemes, based on the channel state, traffic pattern and its own queue status. For example, the source may choose between a direct route to the destination and a relay-assisted scheme. Clearly, due to the difference in the performance achieved, as well as the resources each scheme uses, a sender might wish to choose the most appropriate one based on its status. In this work, we formulate the problem as a Semi-Markov Decision Process. This formulation allows us to find an optimal policy, expressed as a function of the number of packets in the source queue and other parameters. In particular, we show a general solution which covers various configurations, including different packet size distributions and varying channels. Furthermore, for the case of exponential transmission times, we analytically prove the optimal policy has a threshold structure, that is, there is a unique value of a single parameter which determines which scheme (or route) is optimal. Results are also validated with simulations for several interesting models.

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