arXiv subjects

Sennur Ulukus

Publications and source records attributed to Sennur Ulukus.

At least 253 records · Page 14Linked to original sources

arXiv2019

Using Erasure Feedback for Online Timely Updating with an Energy Harvesting Sensor

A real-time status updating system is considered, in which an energy harvesting sensor is acquiring measurements regarding some physical phenomenon and sending them to a destination through an erasure channel. The setting is online, in which energy arrives in units according to a Poisson process with unit rate, with arrival times being revealed causally over time. Energy is saved in a unit-sized battery. The sensor is notified by the destination of whether updates were erased via feedback. Updates need to reach the destination successfully in a timely fashion, namely, such that the long term average age of information, defined as the time elapsed since the latest successful update has reached the destination, is minimized. First, it is shown that the optimal status update policy has a renewal structure: successful update times should constitute a renewal process. Then, threshold-greedy policies are investigated: a new update is transmitted, following a successful one, only if the age of information grows above a certain threshold; and if it is erased, then all subsequent update attempts are greedily scheduled whenever energy is available. The optimal threshold-greedy policy is then analytically derived.

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arXiv2019

Age of Information in Multicast Networks with Multiple Update Streams

We consider the age of information in a multicast network where there is a single source node that sends time-sensitive updates to $n$ receiver nodes. Each status update is one of two kinds: type I or type II. To study the age of information experienced by the receiver nodes for both types of updates, we consider two cases: update streams are generated by the source node at-will and update streams arrive exogenously to the source node. We show that using an earliest $k_1$ and $k_2$ transmission scheme for type I and type II updates, respectively, the age of information of both update streams at the receiver nodes can be made a constant independent of $n$. In particular, the source node transmits each type I update packet to the earliest $k_1$ and each type II update packet to the earliest $k_2$ of $n$ receiver nodes. We determine the optimum $k_1$ and $k_2$ stopping thresholds for arbitrary shifted exponential link delays to individually and jointly minimize the average age of both update streams and characterize the pareto optimal curve for the two ages.

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arXiv2019

Timely Updates in Energy Harvesting Two-hop Networks: Offline and Online Policies

A two-hop energy harvesting communication network is considered, in which measurement updates are transmitted by a source to a destination through an intermediate relay. Updates are to be sent in a timely fashion that minimizes the age of information, defined as the time elapsed since the most recent update at the destination was generated at the source. The source and the relay communicate using energy harvested from nature, which is stored in infinite-sized batteries. Both nodes use fixed transmission rates, and hence updates incur fixed delays (service times). Two problems are formulated: an offline problem, in which the energy arrival information is known a priori, and an online problem, in which such information is revealed causally over time. In both problems, it is shown that it is optimal to transmit updates from the source just in time as the relay is ready to forward them to the destination, making the source and the relay act as one combined node. A recurring theme in the optimal policy is that updates should be as uniformly spread out over time as possible, subject to energy causality and service time constraints. This is perfectly achieved in the offline setting, and is achieved almost surely in the online setting by a best effort policy.

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arXiv2019

Gradient Coding with Clustering and Multi-message Communication

Gradient descent (GD) methods are commonly employed in machine learning problems to optimize the parameters of the model in an iterative fashion. For problems with massive datasets, computations are distributed to many parallel computing servers (i.e., workers) to speed up GD iterations. While distributed computing can increase the computation speed significantly, the per-iteration completion time is limited by the slowest straggling workers. Coded distributed computing can mitigate straggling workers by introducing redundant computations; however, existing coded computing schemes are mainly designed against persistent stragglers, and partial computations at straggling workers are discarded, leading to wasted computational capacity. In this paper, we propose a novel gradient coding (GC) scheme which allows multiple coded computations to be conveyed from each worker to the master per iteration. We numerically show that the proposed GC with multi-message communication (MMC) together with clustering provides significant improvements in the average completion time (of each iteration), with minimal or no increase in the communication load.

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arXiv2019

The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases

We consider private information retrieval (PIR) of a single file out of $K$ files from $N$ non-colluding databases with heterogeneous storage constraints $\mathbf{m}=(m_1, \cdots, m_N)$. The aim of this work is to jointly design the content placement phase and the information retrieval phase in order to minimize the download cost in the PIR phase. We characterize the optimal PIR download cost as a linear program. By analyzing the structure of the optimal solution of this linear program, we show that, surprisingly, the optimal download cost in our heterogeneous case matches its homogeneous counterpart where all databases have the same average storage constraint $μ=\frac{1}{N} \sum_{n=1}^{N} m_n$. Thus, we show that there is no loss in the PIR capacity due to heterogeneity of storage spaces of the databases. We provide the optimum content placement explicitly for $N=3$.

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arXiv2019

Interference Regime Enforcing Rate Maximization for Non-Orthogonal Multiple Access (NOMA)

An interference regime enforcing rate maximization scheme is proposed to maximize the achievable ergodic sum-rate of the parallel Gaussian interference channels by enforcing very strong interference at receivers through power allocation whenever strong interference is observed. Applying successive interference cancellation (SIC) at the receivers, very strong interference can be completely eliminated in this case that enables non-orthogonal multiple access (NOMA). An optimization problem is formulated for ergodic rate maximization, where the conditions for creating very strong interference are included as additional constraints. Then, a generalized iterative waterfilling algorithm is derived to solve this optimization problem. The resulting power allocation scheme is compared in terms of the sum-rate with two other schemes when the interference is treated as noise with optimal or sub-optimal power allocation. The results show that the interference regime enforcing scheme provides major improvement to the sum-rate of parallel Gaussian interference channels and enables NOMA.

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arXiv2018

Private Information Retrieval from Non-Replicated Databases

We consider the problem of private information retrieval (PIR) of a single message out of $K$ messages from $N$ non-colluding and non-replicated databases. Different from the majority of the existing literature, which considers the case of replicated databases where all databases store the same content in the form of all $K$ messages, here, we consider the case of non-replicated databases under a special non-replication structure where each database stores $M$ out of $K$ messages and each message is stored across $R$ different databases. This generates an $R$-regular graph structure for the storage system where the vertices of the graph are the messages and the edges are the databases. We derive a general upper bound for $M=2$ that depends on the graph structure. We then specialize the problem to storage systems described by two special types of graph structures: cyclic graphs and \emph{fully-connected graphs}. We prove that the PIR capacity for the case of cyclic graphs is $\frac{2}{K+1}$, and the PIR capacity for the case of fully-connected graphs is $\min\{\frac{2}{K},\frac{1}{2}\}$. To that end, we propose novel achievable schemes for both graph structures that are capacity-achieving. The central insight in both schemes is to introduce dependency in the queries submitted to databases that do not contain the desired message, such that the requests can be compressed. In both cases, the results show severe degradation in PIR capacity due to non-replication.

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arXiv2018

Age of Information in Multihop Multicast Networks

We consider the age of information in a multihop multicast network where there is a single source node sending time-sensitive updates to $n^L$ end nodes, and $L$ denotes the number of hops. In the first hop, the source node sends updates to $n$ first-hop receiver nodes, and in the second hop each first-hop receiver node relays the update packets that it has received to $n$ further users that are connected to it. This network architecture continues in further hops such that each receiver node in hop $\ell$ is connected to $n$ further receiver nodes in hop $\ell+1$. We study the age of information experienced by the end nodes, and in particular, its scaling as a function of $n$. We show that, using an earliest $k$ transmission scheme in each hop, the age of information at the end nodes can be made a constant independent of $n$. In particular, the source node transmits each update packet to the earliest $k_1$ of the $n$ first-hop nodes, and each first-hop node that receives the update relays it to the earliest $k_2$ out of $n$ second-hop nodes that are connected to it and so on. We determine the optimum $k_\ell$ stopping value for each hop $\ell$ for arbitrary shifted exponential link delays.

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arXiv2018

Minimizing Age of Information with Soft Updates

We consider an information updating system where an information provider and an information receiver engage in an update process over time. Different from the existing literature where updates are countable (hard) and take effect either immediately or after a delay, but $instantaneously$ in both cases, here updates start taking effect right away but $gradually$ over time. We coin this setting $soft$ $updates$. When the updating process starts, the age decreases until the soft update period ends. We constrain the number of times the information provider and the information receiver meet (number of update periods) and the total duration of the update periods. We consider two models for the decrease of age during an update period: In the first model, the rate of decrease of age is proportional to the current age, and in the second model, the rate of decrease of age is constant. The first model results in an exponentially decaying age, and the second model results in a linearly decaying age. In both cases, we determine the optimum updating schemes, by determining the optimum start times and optimum durations of the updates, subject to the constraints on the number of update periods and the total update duration.

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arXiv2018

Scheduling a Human Channel

We consider a system where a human operator processes a sequence of tasks that are similar in nature under a total time constraint. In these systems, the performance of the operator depends on its past utilization. This is akin to $\textit{state-dependent}$ channels where the past actions of the transmitter affects the future quality of the channel (also known as $\textit{action-dependent}$ or $\textit{use-dependent}$ channels). For $\textit{human channels}$, a well-known psychological phenomena, known as $\textit{Yerkes-Dodson law}$, states that a human operator performs worse when he/she is over-utilized or under-utilized. Over such a $\textit{use-dependent}$ human channel, we consider the problem of maximizing a utility function, which is monotonically increasing and concave in the time allocated for each task, under explicit minimum and maximum $\textit{utilization}$ constraints. We show that the optimal solution is to keep the utilization ratio of the operator as high as possible, and to process all the tasks. We prove that the optimal policy consists of two major strategies: utilize the operator without resting until reaching the maximum allowable utilization ratio, and then alternate between working and resting the operator each time reaching the maximum allowable utilization at the end of work-period. We show that even though the tasks are similar in difficulty, the time allocated for the tasks can be different depending on the strategy in which a task is processed; however, the tasks processed in the same strategy are processed equally.

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arXiv2018

The Capacity of Private Information Retrieval from Decentralized Uncoded Caching Databases

We consider the private information retrieval (PIR) problem from decentralized uncoded caching databases. There are two phases in our problem setting, a caching phase, and a retrieval phase. In the caching phase, a data center containing all the $K$ files, where each file is of size $L$ bits, and several databases with storage size constraint $μK L$ bits exist in the system. Each database independently chooses $μK L$ bits out of the total $KL$ bits from the data center to cache through the same probability distribution in a decentralized manner. In the retrieval phase, a user (retriever) accesses $N$ databases in addition to the data center, and wishes to retrieve a desired file privately. We characterize the optimal normalized download cost to be $\frac{D}{L} = \sum_{n=1}^{N+1} \binom{N}{n-1} μ^{n-1} (1-μ)^{N+1-n} \left( 1+ \frac{1}{n} + \dots+ \frac{1}{n^{K-1}} \right)$. We show that uniform and random caching scheme which is originally proposed for decentralized coded caching by Maddah-Ali and Niesen, along with Sun and Jafar retrieval scheme which is originally proposed for PIR from replicated databases surprisingly result in the lowest normalized download cost. This is the decentralized counterpart of the recent result of Attia, Kumar and Tandon for the centralized case. The converse proof contains several ingredients such as interference lower bound, induction lemma, replacing queries and answering string random variables with the content of distributed databases, the nature of decentralized uncoded caching databases, and bit marginalization of joint caching distributions.

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arXiv2018

Distributed Gradient Descent with Coded Partial Gradient Computations

Coded computation techniques provide robustness against straggling servers in distributed computing, with the following limitations: First, they increase decoding complexity. Second, they ignore computations carried out by straggling servers; and they are typically designed to recover the full gradient, and thus, cannot provide a balance between the accuracy of the gradient and per-iteration completion time. Here we introduce a hybrid approach, called coded partial gradient computation (CPGC), that benefits from the advantages of both coded and uncoded computation schemes, and reduces both the computation time and decoding complexity.

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arXiv2018

Age of Information Scaling in Large Networks

We study age of information in a multiple source-multiple destination setting with a focus on its scaling in large wireless networks. There are $n$ nodes that are randomly paired with each other on a fixed area to form $n$ source-destination (S-D) pairs. We propose a three-phase transmission scheme which utilizes local cooperation between the nodes by forming what we call mega update packets to serve multiple S-D pairs at once. We show that under the proposed scheme average age of an S-D pair scales as $O(n^{\frac{1}{4}})$ as the number of users, $n$, in the network grows. To the best of our knowledge, this is the best age scaling result for a multiple source-multiple destination setting.

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arXiv2018

Age of Information in G/G/1/1 Systems

We consider a single server communication setting where the interarrival times of data updates at the source node and the service times to the destination node are arbitrarily distributed. We consider two service discipline models. If a new update arrives when the service is busy, it is dropped in the first model; and it preempts the current update in the second model. For both models, we derive exact expressions for the age of information metric with no restriction on the distributions of interarrival and service times. In addition, we derive upper bounds that are easier to calculate than the exact expressions. In the case with dropping, we also derive a second upper bound by utilizing stochastic ordering if the interarrival times have decreasing mean residual life (DMRL) and service times have new better than use in expectation (NBUE) property.

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arXiv2018

Online Timely Status Updates with Erasures for Energy Harvesting Sensors

An energy harvesting sensor that is sending status updates to a destination through an erasure channel is considered, in which transmissions are prone to being erased with some probability $q$, independently from other transmissions. The sensor, however, is unaware of erasure events due to lack of feedback from the destination. Energy expenditure is normalized in the sense that one transmission consumes one unit of energy. The sensor is equipped with a unit-sized battery to save its incoming energy, which arrives according to a Poisson process of unit rate. The setting is online, in which energy arrival times are only revealed causally after being harvested, and the goal is to design transmission times such that the long term average age of information (AoI), defined as the time elapsed since the latest update has reached the destination successfully, is minimized. The optimal status update policy is first shown to have a renewal structure, in which the time instants at which the destination receives an update successfully constitute a renewal process. Then, for $q\leq\frac{1}{2}$, the optimal renewal policy is shown to have a threshold structure, in which a new status update is transmitted only if the AoI grows above a certain threshold, that is shown to be a decreasing function of $q$. While for $q>\frac{1}{2}$, the optimal renewal policy is shown to be greedy, in which a new status update is transmitted whenever energy is available.

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arXiv2018

Speeding Up Distributed Gradient Descent by Utilizing Non-persistent Stragglers

Distributed gradient descent (DGD) is an efficient way of implementing gradient descent (GD), especially for large data sets, by dividing the computation tasks into smaller subtasks and assigning to different computing servers (CSs) to be executed in parallel. In standard parallel execution, per-iteration waiting time is limited by the execution time of the straggling servers. Coded DGD techniques have been introduced recently, which can tolerate straggling servers via assigning redundant computation tasks to the CSs. In most of the existing DGD schemes, either with coded computation or coded communication, the non-straggling CSs transmit one message per iteration once they complete all their assigned computation tasks. However, although the straggling servers cannot complete all their assigned tasks, they are often able to complete a certain portion of them. In this paper, we allow multiple transmissions from each CS at each iteration in order to make sure a maximum number of completed computations can be reported to the aggregating server (AS), including the straggling servers. We numerically show that the average completion time per iteration can be reduced significantly by slightly increasing the communication load per server.

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arXiv2018

Noisy Private Information Retrieval: On Separability of Channel Coding and Information Retrieval

We consider the problem of noisy private information retrieval (NPIR) from $N$ non-communicating databases, each storing the same set of $M$ messages. In this model, the answer strings are not returned through noiseless bit pipes, but rather through \emph{noisy} memoryless channels. We aim at characterizing the PIR capacity for this model as a function of the statistical information measures of the noisy channels such as entropy and mutual information. We derive a general upper bound for the retrieval rate in the form of a max-min optimization. We use the achievable schemes for the PIR problem under asymmetric traffic constraints and random coding arguments to derive a general lower bound for the retrieval rate. The upper and lower bounds match for $M=2$ and $M=3$, for any $N$, and any noisy channel. The results imply that separation between channel coding and retrieval is optimal except for adapting the traffic ratio from the databases. We refer to this as \emph{almost separation}. Next, we consider the private information retrieval problem from multiple access channels (MAC-PIR). In MAC-PIR, the database responses reach the user through a multiple access channel (MAC) that mixes the responses together in a stochastic way. We show that for the additive MAC and the conjunction/disjunction MAC, channel coding and retrieval scheme are \emph{inseparable} unlike in NPIR. We show that the retrieval scheme depends on the properties of the MAC, in particular on the linearity aspect. For both cases, we provide schemes that achieve the full capacity without any loss due to the privacy constraint, which implies that the user can exploit the nature of the channel to improve privacy. Finally, we show that the full unconstrained capacity is not always attainable by determining the capacity of the selection channel.

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arXiv2018

Novel Decentralized Coded Caching through Coded Prefetching

We propose a new decentralized coded caching scheme for a two-phase caching network, where the data placed in user caches in the prefetching phase are random portions of a maximal distance separable (MDS) coded version of the original files. The proposed scheme achieves a better rate memory trade-off by utilizing the reconstruction property of MDS codes which reduces the number of transmissions that are useful only for a small subset of users in the delivery phase. Unlike the previously available coded prefetching schemes, the proposed scheme does not require to have more users than files. The proposed scheme can be viewed as a generalization of the original uncoded prefetching based decentralized coded caching scheme, and likewise, is applicable to various network topologies.

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