arXiv subjects

Mikael Skoglund

Publications and source records attributed to Mikael Skoglund.

At least 199 records · Page 11Linked to original sources

arXiv2018

A Unified Framework for Training Neural Networks

The lack of mathematical tractability of Deep Neural Networks (DNNs) has hindered progress towards having a unified convergence analysis of training algorithms, in the general setting. We propose a unified optimization framework for training different types of DNNs, and establish its convergence for arbitrary loss, activation, and regularization functions, assumed to be smooth. We show that framework generalizes well-known first- and second-order training methods, and thus allows us to show the convergence of these methods for various DNN architectures and learning tasks, as a special case of our approach. We discuss some of its applications in training various DNN architectures (e.g., feed-forward, convolutional, linear networks), to regression and classification tasks.

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arXiv2018

User Assignment in C-RAN Systems: Algorithms and Bounds

In this work, we investigate the problem of mitigating interference between so called antenna domains of a cloud radio access network (C-RAN). In contrast to previous work, we turn to an approach utilizing primarily the optimal assignment of users to central processors in a C-RAN deployment. We formulate this user assignment problem as an integer optimization problem, and propose an iterative algorithm for obtaining a solution. Motivated by the lack of optimality guarantees on such solutions, we opt to find lower bounds on the problem, and the resulting interference leakage in the network. We thus derive the corresponding Dantzig-Wolfe decomposition, formulate the dual problem, and show that the former offers a tighter bound than the latter. We highlight the fact that the bounds in question consist of linear problems with an exponential number of variables, and adapt the column generation method for solving them. In addition to shedding light on the tightness of the bounds in question, our numerical results show significant sum-rate gains over several comparison schemes. Moreover, the proposed scheme delivers similar performance as W-MMSE with a significantly lower complexity (around 10 times less).

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arXiv2018

Sum-rate Maximization in Sub-28 GHz Millimeter-Wave MIMO Interfering Networks

MIMO systems in the lower part of the millimeter-wave spectrum band (i.e., below 28 GHz) do not exhibit enough directivity and selectively, as their counterparts in higher bands of the spectrum (i.e., above 60 GHz), and thus still suffer from the detrimental effect of interference, on the system sum-rate. As such systems exhibit large numbers of antennas and short coherence times for the channel, traditional methods of distributed coordination are ill-suited, and the resulting communication overhead would offset the gains of coordination. In this work, we propose algorithms for tackling the sum-rate maximization problem, that are designed to address the above limitations. We derive a lower bound on the sum-rate, a so-called DLT bound (i.e., a difference of log and trace), shed light on its tightness, and highlight its decoupled nature at both the transmitters and receivers. Moreover, we derive the solution to each of the subproblems, that we dub non-homogeneous waterfilling (a variation on the MIMO waterfilling solution), and underline an inherent desirable feature: its ability to turn-off streams exhibiting low-SINR, and contribute to greatly speeding up the convergence of the proposed algorithm. We then show the convergence of the resulting algorithm, max-DLT, to a stationary point of the DLT bound. Finally, we rely on extensive simulations of various network configurations, to establish the fast-converging nature of our proposed schemes, and thus their suitability for addressing the short coherence interval, as well as the increased system dimensions, arising when managing interference in lower bands of the millimeter wave spectrum. Moreover, our results also suggest that interference management still brings about significant performance gains, especially in dense deployments.

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arXiv2018

Low-Overhead Coordination in Sub-28 Millimeter-Wave Networks

In this paper, we present some contributions from our recent investigation. We address the open issue of interference coordination for sub-28 GHz millimeter-wave communication, by proposing fast-converging coordination algorithms, for dense multi-user multi-cell networks. We propose to optimize a lower bound on the network sum-rate, after investigating its tightness. The bound in question results in distributed optimization, requiring local information at each base station and user. We derive the optimal solution to the transmit and receive filter updates, that we dub non-homogeneous waterfilling, and show its convergence to a stationary point of the bound. We also underline a built-in mechanism to turn-off data streams with low-SINR, and allocate power to high-SNR streams. This "stream control" is a at the root of the fast-converging nature of the algorithm. Our numerical result conclude that low-overhead coordination offers large gains, for dense sub-$28$ GHz systems. These findings bear direct relevance to the ongoing discussions around 5G New Radio.

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arXiv2018

Golden Angle Modulation: Approaching the AWGN Capacity

In this work, targeting, e.g., future generation cellular, microwave-links, or optical fiber systems, we propose a new geometric shaping design for golden angle modulation (GAM) based on a (double) truncated Gaussian input distribution. The design improves the mutual information (MI), and the peak-to-average power ratio, over the full signal-to-noise ratio (SNR) range relative to two key GAM schemes introduced in [1],[2]. Inspired by the proposed geometric shaping, a simpler, SNR-dependent, design is also suggested. The performance is numerically evaluated with respect to MI and compared with classical modulation schemes. With the proposed design, the SNR can be decreased relative to classical quadrature amplitude modulation, even for relatively modest target spectral efficiencies. As the GAM design can approach the Gaussian channel capacity, the power/energy efficiency is expected to improve.

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arXiv2018

Privacy of Information Sharing Schemes in a Cloud-based Multi-sensor Estimation Problem

In this paper, we consider a multi-sensor estimation problem wherein each sensor collects noisy information about its local process, which is only observed by that sensor, and a common process, which is simultaneously observed by all sensors. The objective is to assess the privacy level of (the local process of) each sensor while the common process is estimated using cloud computing technology. The privacy level of a sensor is defined as the conditional entropy of its local process given the shared information with the cloud. Two information sharing schemes are considered: a local scheme, and a global scheme. Under the local scheme, each sensor estimates the common process based on its the measurement and transmits its estimate to a cloud. Under the global scheme, the cloud receives the sum of sensors' measurements. It is shown that, in the local scheme, the privacy level of each sensor is always above a certain level which is characterized using Shannon's mutual information. It is also proved that this result becomes tight as the number of sensors increases. We also show that the global scheme is asymptotically private, i.e., the privacy loss of the global scheme decreases to zero at the rate of O(1/M) where M is the number of sensors.

math.OC↗

arXiv2017

Progressive Learning for Systematic Design of Large Neural Networks

We develop an algorithm for systematic design of a large artificial neural network using a progression property. We find that some non-linear functions, such as the rectifier linear unit and its derivatives, hold the property. The systematic design addresses the choice of network size and regularization of parameters. The number of nodes and layers in network increases in progression with the objective of consistently reducing an appropriate cost. Each layer is optimized at a time, where appropriate parameters are learned using convex optimization. Regularization parameters for convex optimization do not need a significant manual effort for tuning. We also use random instances for some weight matrices, and that helps to reduce the number of parameters we learn. The developed network is expected to show good generalization power due to appropriate regularization and use of random weights in the layers. This expectation is verified by extensive experiments for classification and regression problems, using standard databases.

cs.NE↗

arXiv2017

Secure Private Information Retrieval from Colluding Databases with Eavesdroppers

The problem of private information retrieval (PIR) is to retrieve one message out of $K$ messages replicated at $N$ databases, without revealing the identity of the desired message to the databases. We consider the problem of PIR with colluding servers and eavesdroppers, named T-EPIR. Specifically, any $T$ out of $N$ databases may collude, i.e. they may communicate their interactions with the user to guess the identity of the requested message. An eavesdropper is curious to know the database and can tap in on the incoming and outgoing transmissions of any $E$ databases. The databases share some common randomness unknown to the eavesdropper and the user, and use the common randomness to generate the answers, such that the eavesdropper can learn no information about the $K$ messages. Define $R^*$ as the optimal ratio of the number of the desired message information bits to the number of total downloaded bits, and $ρ^*$ to be the optimal ratio of the information bits of the shared common randomness to the information bits of the desired file. In our previous work, we found that when $E \geq T$, the optimal ratio that can be achieved equals $1-\frac{E}{N}$. In this work, we focus on the case when $E \leq T$. We derive an outer bound $R^* \leq (1-\frac{T}{N}) \frac{1-\frac{E}{N} \cdot (\frac{T}{N})^{K-1}}{1-(\frac{T}{N})^K}$. We also obtain a lower bound of $ρ^* \geq \frac{\frac{E}{N}(1-(\frac{T}{N})^K)}{(1-\frac{T}{N})(1-\frac{E}{N} \cdot (\frac{T}{N})^{K-1})}$. For the achievability, we propose a scheme which achieves the rate (inner bound) $R=\frac{1-\frac{T}{N}}{1-(\frac{T}{N})^K}-\frac{E}{KN}$. The amount of shared common randomness used in the achievable scheme is $\frac{\frac{E}{N}(1-(\frac{T}{N})^K)}{1-\frac{T}{N}-\frac{E}{KN}(1-(\frac{T}{N})^K)}$ times the file size. The gap between the derived inner and outer bounds vanishes as the number of messages $K$ tends to infinity.

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arXiv2017

Optimal Sensor Design and Zero-Delay Source Coding for Continuous-Time Vector Gauss-Markov Processes

We consider the situation in which a continuous-time vector Gauss-Markov process is observed through a vector Gaussian channel (sensor) and estimated by the Kalman-Bucy filter. Unlike in standard filtering problems where a sensor model is given a priori, we are concerned with the optimal sensor design by which (i) the mutual information between the source random process and the reproduction (estimation) process is minimized, and (ii) the minimum mean-square estimation error meets a given distortion constraint. We show that such a sensor design problem is tractable by semidefinite programming. The connection to zero-delay source-coding is also discussed.

math.OC↗

arXiv2017

The Golden Quantizer: The Complex Gaussian Random Variable Case

The problem of quantizing a circularly-symmetric complex Gaussian random variable is considered. For this purpose, we design two non-uniform quantizers, a high-rate-, and a Lloyd-Max-, quantizer that are both based on the (golden angle) spiral-phyllotaxis packing principle. We find that the proposed schemes have lower mean-square error distortion compared to (non)-uniform polar/rectangular-quantizers, and near-identical to the best performing trained vector quantizers. The proposed quantizer scheme offers a structured design, a simple natural index ordering, and allow for any number of centroids.

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arXiv2017

Linear Symmetric Private Information Retrieval for MDS Coded Distributed Storage with Colluding Servers

The problem of symmetric private information retrieval (SPIR) from a coded database which is distributively stored among colluding servers is studied. Specifically, the database comprises $K$ files, which are stored among $N$ servers using an $(N,M)$-MDS storage code. A user wants to retrieve one file from the database by communicating with the $N$ servers, without revealing the identity of the desired file to any server. Furthermore, the user shall learn nothing about the other $K-1$ files in the database. In the $T$-colluding SPIR problem (hence called TSPIR), any $T$ out of $N$ servers may collude, that is, they may communicate their interactions with the user to guess the identity of the requested file. We show that for linear schemes, the information-theoretic capacity of the MDS-TSPIR problem, defined as the maximum number of information bits of the desired file retrieved per downloaded bit, equals $1-\frac{M+T-1}{N}$, if the servers share common randomness (unavailable at the user) with amount at least $\frac{M+T-1}{N-M-T+1}$ times the file size. Otherwise, the capacity equals zero. We conjecture that our capacity holds also for general MDS-TSPIR schemes.

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arXiv2017

Secure Estimation and Zero-Error Secrecy Capacity

We study the problem of securely estimating the states of an unstable dynamical system subject to nonstochastic disturbances. The estimator obtains all its information through an uncertain channel which is subject to nonstochastic disturbances as well, and an eavesdropper obtains a disturbed version of the channel inputs through a second uncertain channel. An encoder observes and block-encodes the states in such a way that, upon sending the generated codeword, the estimator's error is bounded and such that a security criterion is satisfied ensuring that the eavesdropper obtains as little state information as possible. Two security criteria are considered and discussed with the help of a numerical example. A sufficient condition on the uncertain wiretap channel, i.e., the pair formed by the uncertain channel from encoder to estimator and the uncertain channel from encoder to eavesdropper, is derived which ensures that a bounded estimation error and security are achieved. This condition is also shown to be necessary for a subclass of uncertain wiretap channels. To formulate the condition, the zero-error secrecy capacity of uncertain wiretap channels is introduced, i.e., the maximal rate at which data can be transmitted from the encoder to the estimator in such a way that the eavesdropper is unable to reconstruct the transmitted data. Lastly, the zero-error secrecy capacity of uncertain wiretap channels is studied.

eess.SY↗

arXiv2017

Secure Symmetric Private Information Retrieval from Colluding Databases with Adversaries

The problem of symmetric private information retrieval (SPIR) from replicated databases with colluding servers and adversaries is studied. Specifically, the database comprises $K$ files, which are replicatively stored among $N$ servers. A user wants to retrieve one file from the database by communicating with the $N$ servers, without revealing the identity of the desired file to any server. Furthermore, the user shall learn nothing about the other $K-1$ files. Any $T$ out of $N$ servers may collude, that is, they may communicate their interactions with the user to guess the identity of the requested file. An adversary in the system can tap in on or even try to corrupt the communication. Three types of adversaries are considered: a Byzantine adversary who can overwrite the transmission of any $B$ servers to the user; a passive eavesdropper who can tap in on the incoming and outgoing transmissions of any $E$ servers; and a combination of both -- an adversary who can tap in on a set of any $E$ nodes, and overwrite the transmission of a set of any $B$ nodes. The problems of SPIR with colluding servers and the three types of adversaries are named T-BSPIR, T-ESPIR and T-BESPIR respectively. The capacity of the problem is defined as the maximum number of information bits of the desired file retrieved per downloaded bit. We show that the information-theoretical capacity of T-BSPIR equals $1-\frac{2B+T}{N}$, if the servers share common randomness (unavailable at the user) with amount at least $\frac{2B+T}{N-2B-T}$ times the file size. Otherwise, the capacity equals zero. The capacity of T-ESPIR is proved to equal $1-\frac{\max(T,E)}{N}$, with common randomness at least $\frac{\max(T,E)}{N-\max(T,E)}$ times the file size. Finally, the capacity of T-BESPIR is proved to be $1-\frac{2B+\max(T,E)}{N}$, with common randomness at least $\frac{2B+\max(T,E)}{N-2B-\max(T,E)}$ times the file size.

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arXiv2017

Delay Performance of Wireless Communications with Imperfect CSI and Finite Length Coding

With the rise of critical machine-to-machine applications, next generation wireless communication systems must be designed with strict constraints on the latency and reliability. A key question in this context relates to channel state estimation, which allows the transmitter to adapt the code rate to the channel. In this work, we characterize the trade-off between the estimation sequence length and data codeword length: shorter channel estimation leaves more time for the actual payload transmission but reduces the estimation accuracy and causes more decoding errors. Using lower coding rates can mitigate this effect, but may result in a higher backlog of data at the transmitter. We analyze this trade-off using queueing analysis on top of accurate models of the physical layer, which also account for the finite blocklength of the channel code. Based on a novel closed-form approximation for the error probability given the rate, we show that finding the optimal rate adaptation strategy becomes a convex problem. The optimal rate adaptation strategy and the optimal training sequence length, which both depend on the latency and reliability constraints of the application, can improve the delay performance by an order of magnitude, compared to suboptimal strategies that do not consider those constraints.

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arXiv2017

Directed Information as Privacy Measure in Cloud-based Control

We consider cloud-based control scenarios in which clients with local control tasks outsource their computational or physical duties to a cloud service provider. In order to address privacy concerns in such a control architecture, we first investigate the issue of finding an appropriate privacy measure for clients who desire to keep local state information as private as possible during the control operation. Specifically, we justify the use of Kramer's notion of causally conditioned directed information as a measure of privacy loss based on an axiomatic argument. Then we propose a methodology to design an optimal "privacy filter" that minimizes privacy loss while a given level of control performance is guaranteed. We show in particular that the optimal privacy filter for cloud-based Linear-Quadratic-Gaussian (LQG) control can be synthesized by a Linear-Matrix-Inequality (LMI) algorithm. The trade-off in the design is illustrated by a numerical example.

math.OC↗

arXiv2016

The Matrix Exponential Distribution - A Tool for Wireless System Performance Analysis

In [1], we introduced a new, matrix algebraic, performance analysis framework for wireless systems with fading channels based on the matrix exponential distribution. The main idea was to use the compact, powerful, and easy-to-use, matrix exponential (ME)-distribution for i) modeling the unprocessed channel signal to noise ratio (SNR), ii) exploiting the closure property of the ME-distribution for SNR processing operations to give the effective channel random variable (r.v.) on ME-distribution form, and then to iii) express the performance measure in a closed-form based on ME-distribution matrix/vector parameters only. In this work, we aim to more clearly present, formalize, refine and develop this unified bottom-up analysis framework, show its versatility to handle important communication cases, performance evaluation levels, and performance metrics. The bivariate ME-distribution is introduced here as yet another useful ME-tool, e.g. to account for dependency among two r.v.s. We propose that the ME-distribution may, in addition to fading, also characterize the pdf of discrete-time signal r.v.s, thus extending the ME-distribution matrix form to new generalized 1D/2D-Gaussian-, and Rayleigh-, distribution-like matrix forms. Our findings here, strengthen the observation from [1], [2], and indicates that the ME-distribution can be a promising tool for wireless system modeling and performance analysis.

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arXiv2016

Massive MIMO Pilot Retransmission Strategies for Robustification against Jamming

This letter proposes anti-jamming strategies based on pilot retransmission for a single user uplink massive MIMO under jamming attack. A jammer is assumed to attack the system both in the training and data transmission phases. We first derive an achievable rate which enables us to analyze the effect of jamming attacks on the system performance. Counter-attack strategies are then proposed to mitigate this effect under two different scenarios: random and deterministic jamming attacks. Numerical results illustrate our analysis and benefit of the proposed schemes.

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arXiv2016

Symmetric Private Information Retrieval For MDS Coded Distributed Storage

A user wants to retrieve a file from a database without revealing the identity of the file retrieved at the database, which is known as the problem of private information retrieval (PIR). If it is further required that the user obtains no information about the database other than the desired file, the concept of symmetric private information retrieval (SPIR) is introduced to guarantee privacy for both parties. In this paper, the problem of SPIR is studied for a database stored among $N$ nodes in a distributed way, by using an $(N,M)$-MDS storage code. The information-theoretic capacity of SPIR, defined as the maximum number of symbols of the desired file retrieved per downloaded symbol, for the coded database is derived. It is shown that the SPIR capacity for coded database is $1-\frac{M}{N}$, when the amount of the shared common randomness of distributed nodes (unavailable at the user) is at least $\frac{M}{N-M}$ times the file size. Otherwise, the SPIR capacity for the coded database equals zero.

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