Linear Transmission of Composite Gaussian Measurements over a Fading Channel under Delay Constraints

Delay constrained linear transmission (LT) strategies are considered for the transmission of composite Gaussian measurements over an additive white Gaussian noise fading channel under an average power constraint. If the channel state information (CSI) is known by both the encoder and decoder, the optimal LT scheme in terms of the average mean-square error distortion is characterized under a strict delay constraint, and a graphical interpretation of the optimal power allocation strategy is presented. Then, for general delay constraints, two LT strategies are proposed based on the solution to a particular multiple measurements-parallel channels scenario. It is shown that the distortion decreases as the delay constraint is relaxed, and when the delay constraint is completely removed, both strategies achieve the optimal performance under certain matching conditions. If the CSI is known only by the decoder, the optimal LT strategy is derived under a strict delay constraint. The extension to general delay constraints is elusive. As a first step towards understanding the structure of the optimal scheme in this case, it is shown that for the multiple measurementsparallel channels scenario, any LT scheme that uses only a oneto-one linear mapping between measurements and channels is suboptimal in general

Privacy-cost trade-offs in demand-side management with storage

Demand-side energy management (EM) is studied from a privacy-cost trade-off perspective, considering time-of-use pricing and the presence of an energy storage unit. Privacy i s measured as the variation of the power withdrawn from the gri d from a fixed target value. Assuming non-causal knowledge of t he household’s aggregate power demand profile and the electric ity prices at the energy management unit (EMU), the privacy-cos t trade-off is formulated as a convex optimization problem, a nd a low-complexity backward water-filling algorithm is proposed to compute the optimal EM policy. The problem is studied also in the online setting assuming that the power demand profile is known to the EMU only causally, and the optimal EM policy is obtained numerically through dynamic programming (DP). Du e to the high computational cost of DP, a low-complexity heuri stic EM policy with a performance close to the optimal online solu tion is also proposed, exploiting the water-filling algorithm ob tained in the offline setting. As an alternative, information theor etic leakage rate is also evaluated, and shown to follow a similar trend as the load variance, which supports the validity of th e load variance as a measure of privacy. Finally, the privacy- cost trade-off, and the impact of the size of the storage unit on th is trade-off are studied through numerical simulations using real smart meter data in both the offline and online settings

Bivariate polynomial coding for efficient distributed matrix multiplication

Coded computing is an effective technique to mitigate “stragglers” in large-scale and distributed matrix multiplication. In particular, univariate polynomial codes have been shown to be effective in straggler mitigation by making the computation time depend only on the fastest workers. However, these schemes completely ignore the work done by the straggling workers resulting in a waste of computational resources. To reduce the amount of work left unfinished at workers, one can further decompose the matrix multiplication task into smaller sub-tasks, and assign multiple sub-tasks to each worker, possibly heterogeneously, to better fit their particular storage and computation capacities. In this work, we propose a novel family of bivariate polynomial codes to efficiently exploit the work carried out by straggling workers. We show that bivariate polynomial codes bring significant advantages in terms of upload communication costs and storage efficiency, measured in terms of the number of sub-tasks that can be computed per worker. We propose two bivariate polynomial coding schemes. The first one exploits the fact that bivariate interpolation is always possible on a rectangular grid of evaluation points. We obtain such points at the cost of adding some redundant computations. For the second scheme, we relax the decoding constraints and require decodability for almost all choices of the evaluation points. We present interpolation sets satisfying such decodability conditions for certain storage configurations of workers. Our numerical results show that bivariate polynomial coding considerably reduces the average computation time of distributed matrix multiplication. We believe this work opens up a new class of previously unexplored coding schemes for efficient coded distributed computation

Wireless Content Caching for Small Cell and D2D Networks

The fifth generation wireless networks must provide fast and reliable connectivity while coping with the ongoing traffic growth. It is of paramount importance that the required resources, such as energy and bandwidth, do not scale with traffic. While the aggregate network traffic is growing at an unprecedented rate, users tend to request the same popular contents at different time instants. Therefore, caching the most popular contents at the network edge is a promising solution to reduce the traffic and the energy consumption over the backhaul links. In this paper, two scenarios are considered, where caching is performed either at a small base station, or directly at the user terminals, which communicate using Device-to-Device (D2D) communications. In both scenarios, joint design of the transmission and caching policies is studied when the user demands are known in advance. This joint design offers two different caching gains, namely, the pre-downloading and local caching gains. It is shown that the finite cache capacity limits the attainable gains, and creates an inherent tradeoff between the two types of gains. In this context, a continuous time optimization problem is formulated to determine the optimal transmission and caching policies that minimize a generic cost function, such as energy, bandwidth, or throughput. The jointly optimal solution is obtained by demonstrating that caching files at a constant rate is optimal, which allows reformulation of the problem as a finite-dimensional convex program. The numerical results show that the proposed joint transmission and caching policy dramatically reduces the total cost, which is particularised to the total energy consumption at the Macro Base Station (MBS), as well as to the total economical cost for the service provider, when users demand economical incentives for delivering content to other users over the D2D links

Bivariate polynomial codes for secure distributed matrix multiplication

We consider the problem of secure distributed matrix multiplication (SDMM). Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against workers and boosting the computation speed by efficiently mitigating stragglers. In this work, we present a non-direct secure extension of the recently introduced bivariate polynomial codes. Bivariate polynomial codes have been shown to be able to further speed up distributed matrix multiplication by exploiting the partial work done by the stragglers rather than completely ignoring them while reducing the upload communication cost and/or the workers’ storage’s capacity needs. We show that, especially for upload communication or storage constrained settings, the proposed approach reduces the average computation time of SDMM compared to its competitors in the literature

Smart meter privacy for multiple users in the presence of an alternative energy source

Smart meters (SMs) measure and report users' energy consumption to the utility provider (UP) in almost real-time, providing a much more detailed depiction of the consumer's energy consumption compared to their analog counterparts. This increased rate of information flow to the UP, together with its many potential benefits, raise important concerns regarding user privacy. This paper investigates, from an information theoretic perspective, the privacy that can be achieved in a multiuser SM system in the presence of an alternative energy source (AES). To measure privacy, we use the mutual information rate between the users' real energy consumption profile and SM readings that are available to the UP. The objective is to characterize the privacy-power function, defined as the minimal information leakage rate that can be obtained with an average power-limited AES. We characterize the privacy-power function in a single letter form when the users' energy demands are assumed to be independent and identically distributed over time. Moreover, for binary and exponentially distributed energy demands, we provide an explicit characterization of the privacy-power function. For any discrete energy demands, we demonstrate that the privacy-power function can always be efficiently evaluated numerically. Finally, for continuous energy demands, we derive an explicit lower bound on the privacy-power function, which is tight for exponentially distributed loads

Privacy of smart meter systems with an alternative energy source

Smart meter (SM) measurements provide near realtime information on the electricity consumption of a user to the utility provider (UP). This data can be used to extract private information on the energy consumption patterns of the user. Assuming that the user has access to an alternative energy source (AES) in addition to the power grid, SM privacy problem is studied from an information theoretic perspective. The energy requirement of the user (input load) at each time instant can be satisfied either from the power grid (output load) or from the AES. It is assumed that the output load can be perfectly tracked by the UP, and the privacy is measured through the information leakage rate. For given average and peak power constraints on the AES, privacy-power function is defined, and its equivalence to the rate-distortion function with a difference distortion measure is shown. Focusing on continuous input loads, the privacy-power function is characterized when there is only peak power limitation on the AES, while the Shannon lower bound is provided for the general case. The bound is shown to be achievable for the exponential input distribution. © 2013 IEEE

Competitive analysis of energy harvesting wireless communication systems

A competitive analysis for the online and offline optimization problems for a slotted energy harvesting (EH) wireless communication system is studied. The objective is to design online strategies that minimize the competitive rate gap that is defined as the maximum gap between the optimal rates that can be achieved by the offline and online policies over all possible energy arrival profiles. It is shown that the competitive rate gap is upper-bounded by the logarithm of the number of slots, and a myopic online transmission policy is proposed that achieves a lower rate gap

Bivariate Polynomial Coding for Straggler Exploitation with Heterogeneous Workers

Polynomial coding has been proposed as a solution to the straggler mitigation problem in distributed matrix multiplication. Previous works employ univariate polynomials to encode matrix partitions. Such schemes greatly improve the speed of distributed computing systems by making the task completion time to depend only on the fastest workers. However, they completely ignore the work done by the slowest workers resulting in inefficient use of computing resources. In order to exploit the partial computations of the slower workers, we further decompose the overall matrix multiplication task into even smaller subtasks, and we propose bivariate polynomial codes. We show that these codes are a more natural choice to accommodate the additional decomposition of subtasks, and to exploit the heterogeneous storage and computation resources at workers. However, in contrast to univariate polynomial decoding, guarantying decodability with multivariate interpolation is much harder. We propose two bivariate polynomial coding schemes and study their decodability conditions. Our numerical results show that bivariate polynomial coding considerably reduces the computation time of distributed matrix multiplication

Optimal privacy-cost trade-off in demand-side management with storage

Demand-side energy storage management is studied from a joint privacy-energy cost optimization perspective. Assuming that the user's power demand profile as well as the electricity prices are known non-causally, the optimal energy management (EM) policy that jointly increases the privacy of the user and reduces his energy cost is characterized. The backward water-filling interpretation is provided for the optimal EM policy. While the energy cost is reduced by requesting more energy when the prices are lower, energy consumption privacy is achieved by a smoother output load. It is shown that both gains can be achieved by using a limited size storage unit. The optimal trade-off between the user's privacy and energy cost is characterized, and the impact of the size of the storage unit and the resolution of the smart meter readings on this trade-off is studied