arXiv subjects

Emina Soljanin

Publications and source records attributed to Emina Soljanin.

At least 37 records · Page 2Linked to original sources

arXiv2023

QKD Based on Time-Entangled Photons and its Key-Rate Promise

For secure practical systems, quantum key distribution (QKD) must provide high key rates over long distances. Time-entanglement-based QKD promises to increase the secret key rate and distribution distances compared to other QKD implementations. This article describes the major steps in QKD protocols, focusing on the nascent QKD technology based on high-dimensional time-bin entangled photons. We overview state-of-the-art from the information and coding theory perspective. In particular, we discuss the key rate loss due to single-photon detector imperfections. We hope the open questions posed and discussed in this paper will inspire information and coding theorists to contribute to and impact fledgling quantum applications and influence future quantum communication systems.

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arXiv2023

Information Rates with Non Ideal Photon Detectors in Time-Entanglement Based QKD

We develop new methods of quantifying the impact of photon detector imperfections on achievable secret key rates in Time-Entanglement based Quantum Key Distribution (QKD). We address photon detection timing jitter, detector downtime, and photon dark counts and show how each may decrease the maximum achievable secret key rate in different ways. We begin with a standard Discrete Memoryless Channel (DMC) model to get a good bound on the mutual information lost due to the timing jitter, then introduce a novel Markov Chain (MC) based model to characterize the effect of detector downtime and show how it introduces memory to the key generation process. Finally, we propose a new method of including dark counts in the analysis that shows how dark counts can be especially detrimental when using the common Pulse Position Modulation (PPM) for key generation. Our results show that these three imperfections can significantly reduce the achievable secret key rate when using PPM for QKD. Additionally, one of our main results is providing tooling for experimentalists to predict their systems' achievable secret key rate given the detector specifications.

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arXiv2023

Time-Entanglement QKD: Secret Key Rates and Information Reconciliation Coding

In time entanglement-based quantum key distribution (QKD), Alice and Bob extract the raw key bits from the (identical) arrival times of entangled photon pairs by time-binning. Each of them individually discretizes time into bins and groups them into frames. They retain only the frames with a single occupied bin. Thus, Alice and Bob can use the position of the occupied bin within a frame to generate random key bits, as in PPM modulation. Because of entanglement, their occupied bins and their keys should be identical. However, practical photon detectors suffer from time jitter errors. These errors cause discrepancies between Alice's and Bob's keys. Alice sends information to Bob through the public channel to reconcile the keys. The amount of information determines the secret key rate. This paper computes the secret key rates possible with detector jitter errors and constructs codes for information reconciliation to approach these rates.

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arXiv2022

Dual-Code Bounds on Multiple Concurrent (Local) Data Recovery

We are concerned with linear redundancy storage schemes regarding their ability to provide concurrent (local) recovery of multiple data objects. This paper initiates a study of such systems within the classical coding theory. We show how we can use the structural properties of the generator matrix defining the scheme to obtain a bounding polytope for the set of data access rates the system can support. We derive two dual distance outer bounds, which are sharp for some large classes of matrix families.

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arXiv2022

Balanced Nonadaptive Redundancy Scheduling

Distributed computing systems implement redundancy to reduce the job completion time and variability. Despite a large body of work about computing redundancy, the analytical performance evaluation of redundancy techniques in queuing systems is still an open problem. In this work, we take one step forward to analyze the performance of scheduling policies in systems with redundancy. In particular, we study the pattern of shared servers among replicas of different jobs. To this end, we employ combinatorics and graph theory and define and derive performance indicators using the statistics of the overlaps. We consider two classical nonadaptive scheduling policies: random and round-robin. We then propose a scheduling policy based on combinatorial block designs. Compared with conventional scheduling, the proposed scheduling improves the performance indicators. We study the expansion property of the graphs associated with round-robin and block design-based policies. It turns out the superior performance of the block design-based policy results from better expansion properties of its associated graph. As indicated by the performance indicators, the simulation results show that the block design-based policy outperforms random and round-robin scheduling in different scenarios. Specifically, it reduces the average waiting time in the queue to up to 25% compared to the random policy and up to 100% compared to the round-robin policy.

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arXiv2021

Covert, Low-Delay, Coded Message Passing in Mobile (IoT) Networks

We introduce a gossip-like protocol for covert message passing between Alice and Bob as they move in an area watched over by a warden Willie. The area hosts a multitude of Internet of (Battlefield) Things (Io\b{eta}T) objects. Alice and Bob perform random walks on a random regular graph. The Io\b{eta}T objects reside on the vertices of this graph, and some can serve as relays between Alice and Bob. The protocol starts with Alice splitting her message into small chunks, which she can covertly deposit to the relays she encounters. The protocol ends with Bob collecting the chunks. Alice may encode her data before the dissemination. Willie can either perform random walks as Alice and Bob do or conduct uniform surveillance of the area. In either case, he can only observe one relay at a time. We evaluate the system performance by the covertness probability and the message passing delay. In our protocol, Alice splits her message to increase the covertness probability and adds (coded) redundancy to reduce the transmission delay. The performance metrics depend on the graph, communications delay, and code parameters. We show that, in most scenarios, it is impossible to find the design parameters that simultaneously maximize the covertness probability and minimize the message delay.

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arXiv2021

Diversity/Parallelism Trade-off in Distributed Systems with Redundancy

As numerous machine learning and other algorithms increase in complexity and data requirements, distributed computing becomes necessary to satisfy the growing computational and storage demands, because it enables parallel execution of smaller tasks that make up a large computing job. However, random fluctuations in task service times lead to straggling tasks with long execution times. Redundancy, in the form of task replication and erasure coding, provides diversity that allows a job to be completed when only a subset of redundant tasks is executed, thus removing the dependency on the straggling tasks. In situations of constrained resources (here a fixed number of parallel servers), increasing redundancy reduces the available resources for parallelism. In this paper, we characterize the diversity vs. parallelism trade-off and identify the optimal strategy, among replication, coding and splitting, which minimizes the expected job completion time. We consider three common service time distributions and establish three models that describe scaling of these distributions with the task size. We find that different distributions with different scaling models operate optimally at different levels of redundancy, and thus may require very different code rates.

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arXiv2021

Distributed Storage Allocations for Optimal Service Rates

Redundant storage maintains the performance of distributed systems under various forms of uncertainty. This paper considers the uncertainty in node access and download service. We consider two access models under two download service models. In one access model, a user can access each node with a fixed probability, and in the other, a user can access a random fixed-size subset of nodes. We consider two download service models. In the first (small file) model, the randomness associated with the file size is negligible. In the second (large file) model, randomness is associated with both the file size and the system's operations. We focus on the service rate of the system. For a fixed redundancy level, the systems' service rate is determined by the allocation of coded chunks over the storage nodes. We consider quasi-uniform allocations, where coded content is uniformly spread among a subset of nodes. The question we address asks what the size of this subset (spreading) should be. We show that in the small file model, concentrating the coded content to a minimum-size subset is universally optimal. For the large file model, the optimal spreading depends on the system parameters. These conclusions hold for both access models.

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arXiv2021

Service Rate Region: A New Aspect of Coded Distributed System Design

Erasure coding has been recognized as a powerful method to mitigate delays due to slow or straggling nodes in distributed systems. This work shows that erasure coding of data objects can flexibly handle skews in the request rates. Coding can help boost the \emph{service rate region}, that is, increase the overall volume of data access requests that the system can handle. This paper aims to postulate the service rate region as an important consideration in the design of erasure-coded distributed systems. We highlight several open problems that can be grouped into two broad threads: 1) characterizing the service rate region of a given code and finding the optimal request allocation, and2) designing the underlying erasure code for a given service rate region. As contributions along the first thread, we characterize the rate regions of maximum-distance-separable, locally repairable, and Simplex codes. We show the effectiveness of hybrid codes that combine replication and erasure coding in terms of code design. We also discover fundamental connections between multi-set batch codes and the problem of maximizing the service rate region.

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arXiv2021

Download Time Analysis for Distributed Storage Codes with Locality and Availability

The paper presents techniques for analyzing the expected download time in distributed storage systems that employ systematic availability codes. These codes provide access to hot data through the systematic server containing the object and multiple recovery groups. When a request for an object is received, it can be replicated (forked) to the systematic server and all recovery groups. We first consider the low-traffic regime and present the close-form expression for the download time. By comparison across systems with availability, maximum distance separable (MDS), and replication codes, we demonstrate that availability codes can reduce download time in some settings but are not always optimal. In the high-traffic regime, the system consists of multiple inter-dependent Fork-Join queues, making exact analysis intractable. Accordingly, we present upper and lower bounds on the download time, and an M/G/1 queue approximation for several cases of interest. Via extensive numerical simulations, we evaluate our bounds and demonstrate that the M/G/1 queue approximation has a high degree of accuracy.

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arXiv2021

Evaluating Load Balancing Performance in Distributed Storage with Redundancy

To facilitate load balancing, distributed systems store data redundantly. We evaluate the load balancing performance of storage schemes in which each object is stored at $d$ different nodes, and each node stores the same number of objects. In our model, the load offered for the objects is sampled uniformly at random from all the load vectors with a fixed cumulative value. We find that the load balance in a system of $n$ nodes improves multiplicatively with $d$ as long as $d = o\left(\log(n)\right)$, and improves exponentially once $d = Θ\left(\log(n)\right)$. We show that the load balance improves in the same way with $d$ when the service choices are created with XOR's of $r$ objects rather than object replicas. In such redundancy schemes, storage overhead is reduced multiplicatively by $r$. However, recovery of an object requires downloading content from $r$ nodes. At the same time, the load balance increases additively by $r$. We express the system's load balance in terms of the maximal spacing or maximum of $d$ consecutive spacings between the ordered statistics of uniform random variables. Using this connection and the limit results on the maximal $d$-spacings, we derive our main results.

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arXiv2020

Efficient Replication for Straggler Mitigation in Distributed Computing

Master-worker distributed computing systems use task replication in order to mitigate the effect of slow workers, known as stragglers. Tasks are grouped into batches and assigned to one or more workers for execution. We first consider the case when the batches do not overlap and, using the results from majorization theory, show that, for a general class of workers' service time distributions, a balanced assignment of batches to workers minimizes the average job compute time. We next show that this balanced assignment of non-overlapping batches achieves lower average job compute time compared to the overlapping schemes proposed in the literature. Furthermore, we derive the optimum redundancy level as a function of the service time distribution at workers. We show that the redundancy level that minimizes average job compute time is not necessarily the same as the redundancy level that maximizes the predictability of job compute time, and thus there exists a trade-off between optimizing the two metrics. Finally, by running experiments on Google cluster traces, we observe that redundancy can reduce the compute time of the jobs in Google clusters by an order of magnitude, and that the optimum level of redundancy depends on the distribution of tasks' service time.

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arXiv2020

Efficient Storage Schemes for Desired Service Rate Regions

A major concern in cloud/edge storage systems is serving a large number of users simultaneously. The service rate region is introduced recently as an important performance metric for coded distributed systems, which is defined as the set of all data access requests that can be simultaneously handled by the system. This paper studies the problem of designing a coded distributed storage system storing k files where a desired service rate region R of the system is given and the goal is 1) to determine the minimum number of storage nodes n(R) (or a lower bound on n(R)) for serving all demand vectors inside the set R and 2) to design the most storage-efficient redundancy scheme with the service rate region covering R. Towards this goal, we propose three general lower bounds for n(R). Also, for k=2, we characterize n(R), i.e., we show that the proposed lower bounds are tight via designing a novel storage-efficient redundancy scheme with n(R) storage nodes and the service rate region covering R.

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arXiv2020

Quantum Information Processing: An Essential Primer

Quantum information science is an exciting, wide, rapidly progressing, cross-disciplinary field, and that very nature makes it both attractive and hard to enter. In this primer, we first provide answers to the three essential questions that any newcomer needs to know: How is quantum information represented? How is quantum information processed? How is classical information extracted from quantum states? We then introduce the most basic quantum information theoretic notions concerning entropy, sources, and channels, as well as secure communications and error correction. We conclude with examples that illustrate the power of quantum correlations. No prior knowledge of quantum mechanics is assumed.

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arXiv2020

Data Freshness in Leader-Based Replicated Storage

Leader-based data replication improves consistency in highly available distributed storage systems via sequential writes to the leader nodes. After a write has been committed by the leaders, follower nodes are written by a multicast mechanism and are only guaranteed to be eventually consistent. With Age of Information (AoI) as the freshness metric, we characterize how the number of leaders affects the freshness of the data retrieved by an instantaneous read query. In particular, we derive the average age of a read query for a deterministic model for the leader writing time and a probabilistic model for the follower writing time. We obtain a closed-form expression for the average age for exponentially distributed follower writing time. Our numerical results show that, depending on the relative speed of the write operation to the two groups of nodes, there exists an optimal number of leaders which minimizes the average age of the retrieved data, and that this number increases as the relative speed of writing on leaders increases.

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arXiv2020

Increasing the Raw Key Rate in Energy-Time Entanglement Based Quantum Key Distribution

A Quantum Key Distribution (QKD) protocol describes how two remote parties can establish a secret key by communicating over a quantum and a public classical channel that both can be accessed by an eavesdropper. QKD protocols using energy-time entangled photon pairs are of growing practical interest because of their potential to provide a higher secure key rate over long distances by carrying multiple bits per entangled photon pair. We consider a system where information can be extracted by measuring random times of a sequence of entangled photon arrivals. Our goal is to maximize the utility of each such pair. We propose a discrete time model for the photon arrival process, and establish a theoretical bound on the number of raw bits that can be generated under this model. We first analyse a well known simple binning encoding scheme, and show that it generates significantly lower information rate than what is theoretically possible. We then propose three adaptive schemes that increase the number of raw bits generated per photon, and compute and compare the information rates they offer. Moreover, the effect of public channel communication on the secret key rates of the proposed schemes is investigated.

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arXiv2020

A Geometric View of the Service Rates of Codes Problem and its Application to the Service Rate of the First Order Reed-Muller Codes

Service rate is an important, recently introduced, performance metric associated with distributed coded storage systems. Among other interpretations, it measures the number of users that can be simultaneously served by the storage system. We introduce a geometric approach to address this problem. One of the most significant advantages of this approach over the existing approaches is that it allows one to derive bounds on the service rate of a code without explicitly knowing the list of all possible recovery sets. To illustrate the power of our geometric approach, we derive upper bounds on the service rates of the first order Reed-Muller codes and simplex codes. Then, we show how these upper bounds can be achieved. Furthermore, utilizing the proposed geometric technique, we show that given the service rate region of a code, a lower bound on the minimum distance of the code can be obtained.

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arXiv2020

A Combinatorial View of the Service Rates of Codes Problem, its Equivalence to Fractional Matching and its Connection with Batch Codes

We propose a novel technique for constructing a graph representation of a code through which we establish a significant connection between the service rate problem and the well-known fractional matching problem. Using this connection, we show that the service capacity of a coded storage system equals the fractional matching number in the graph representation of the code, and thus is lower bounded and upper bounded by the matching number and the vertex cover number, respectively. This is of great interest because if the graph representation of a code is bipartite, then the derived upper and lower bounds are equal, and we obtain the capacity. Leveraging this result, we characterize the service capacity of the binary simplex code whose graph representation, as we show, is bipartite. Moreover, we show that the service rate problem can be viewed as a generalization of the multiset primitive batch codes problem.

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