Soheil Mohajer

Smart Meter Privacy: A Theoretical Framework

The solutions offered to-date for end-user privacy in smart meter measurements, a well-known challenge in the smart grid, have been tied to specific technologies such as batteries or assumptions on data usage without quantifying the loss of benefit (utility) that results from any such approach. Using tools from information theory and a hidden Markov model for the measurements, a new framework is presented that abstracts both the privacy and the utility requirements of smart meter data. This leads to a novel privacy-utility tradeoff problem with minimal assumptions that is tractable. For a stationary Gaussian model of the electricity load, it is shown that for a desired mean-square distortion (utility) measure between the measured and revealed data, the optimal privacy-preserving solution: i) exploits the presence of high-power but less private appliance spectra as implicit distortion noise, and ii) filters out frequency components with lower power relative to a distortion threshold; this approach encompasses many previously proposed approaches to smart meter privacy.

Smart meter privacy: A utility-privacy framework

End-user privacy in smart meter measurements is a well-known challenge in the smart grid. The solutions offered thus far have been tied to specific technologies such as batteries or assumptions on data usage. Existing solutions have also not quantified the loss of benefit (utility) that results from any such privacy-preserving approach. Using tools from information theory, a new framework is presented that abstracts both the privacy and the utility requirements of smart meter data. This leads to a novel privacy-utility tradeoff problem with minimal assumptions that is tractable. Specifically for a stationary Gaussian Markov model of the electricity load, it is shown that the optimal utility-and-privacy preserving solution requires filtering out frequency components that are low in power, and this approach appears to encompass most of the proposed privacy approaches.

Transmission techniques for relay-interference networks

In this paper we study the relay-interference wireless network, in which relay (helper) nodes are to facilitate competing information flows over a wireless network. We examine this in the context of a deterministic wireless interaction model, which eliminates the channel noise and focuses on the signal interactions. Using this model, we show that almost all the known schemes such as interference suppression, interference alignment and interference separation are necessary for relay-interference networks. In addition, we discover a new interference management technique, which we call interference neutralization, which allows for over-the-air interference removal, without the transmitters having complete access the interfering signals. We show that interference separation, suppression, and neutralization arise in a fundamental manner, since we show complete characterizations for special configurations of the relay-interference network.

Approximate Capacity of a Class of Gaussian Interference-Relay Networks

In this paper, we study a Gaussian relay-interference network, in which relay (helper) nodes are to facilitate competing information flows between different source-destination pairs. We focus on two-stage relay-interference networks where there are weak cross links, causing the networks to behave like a chain of Z Gaussian channels. Our main result is an approximate characterization of the capacity region for such ZZ and ZS networks. We propose a new interference management scheme, termed interference neutralization, which is implemented using structured lattice codes. This scheme allows for over-the-air interference removal, without the transmitters having complete access the interfering signals. This scheme in conjunction a new network decomposition technique provides the approximate characterization. Our analysis of these Gaussian networks is based on insights gained from an exact characterization of the corresponding linear deterministic model.

Graph-Constrained Group Testing

Nonadaptive group testing involves grouping arbitrary subsets of n items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most d defective items. Motivated by applications in network tomography, sensor networks and infection propagation, a variation of group testing problems on graphs is formulated. Unlike conventional group testing problems, each group here must conform to the constraints imposed by a graph. For instance, items can be associated with vertices and each pool is any set of nodes that must be path connected. In this paper, a test is associated with a random walk. In this context, conventional group testing corresponds to the special case of a complete graph on n vertices. For interesting classes of graphs a rather surprising result is obtained, namely, that the number of tests required to identify d defective items is substantially similar to what is required in conventional group testing problems, where no such constraints on pooling is imposed. Specifically, if T(n) corresponds to the mixing time of the graph G, it is shown that with m = O(d2T2(n) log(n/d)) nonadaptive tests, one can identify the defective items. Consequently, for the Erdos-Rényi random graph G(n, p), as well as expander graphs with constant spectral gap, it follows that m = O(d2 log3 n) non-adaptive tests are sufficient to identify d defective items. Next, a specific scenario is considered that arises in network tomography, for which it is shown that m = O(d3 log3 n) nonadaptive tests are sufficient to identify d defective items. Noisy counterparts of the graph constrained group testing problem are considered, for which parallel results are developed. We also briefly discuss extensions to compressive sensing on graphs.

Approximating the Gaussian Multiple Description Rate Region Under Symmetric Distortion Constraints

We consider multiple description (MD) coding for the Gaussian source with K descriptions under the symmetric mean-squared error (MSE) distortion constraints, and provide an approximate characterization of the rate region. We show that the rate region can be sandwiched between two polytopes, between which the gap can be upper-bounded by constants dependent on the number of descriptions, but independent of the distortion constraints. Underlying this result is an exact characterization of the lossless multilevel diversity source coding problem: a lossless counterpart of the MD problem. This connection provides a polytopic template for the inner and outer bounds to the rate region. In order to establish the outer bound, we generalize Ozarows technique to introduce a strategic expansion of the original probability space by more than one random variable. For the symmetric rate case with any number of descriptions, we show that the gap between the upper bound and the lower bound for the individual description rate-distortion function is no larger than 0.92 bit. The results developed in this work also suggest that the ldquoseparationrdquo approach of combining successive refinement quantization and lossless multilevel diversity coding is a competitive one, since its performance is only a constant away from the optimum. The results are further extended to general sources under the MSE distortion measure, where a similar but looser bound on the gap holds.

Degrees of Freedom Region of the MIMO Interference Channel With Output Feedback and Delayed CSIT

The two-user multiple-input multiple-output (MIMO) interference channel (IC) with arbitrary numbers of antennas at each terminal is considered and the degrees of freedom (DoF) region is characterized in the presence of noiseless channel output feedback from each receiver to its respective transmitter and availability of delayed channel state information at the transmitters (CSIT). It is shown that having output feedback and delayed CSIT can strictly enlarge the DoF region of the MIMO IC when compared to the case in which only delayed CSIT is present. The proposed coding schemes that achieve the corresponding DoF region with feedback and delayed CSIT utilize both resources, i.e., feedback and delayed CSIT in a nontrivial manner. It is also shown that the DoF region with local feedback and delayed CSIT is equal to the DoF region with global feedback and delayed CSIT, i.e., local feedback and delayed CSIT is equivalent to global feedback and delayed CSIT from the perspective of the DoF region. The converse is proved for a stronger setting in which the channels to the two receivers need not be statistically equivalent.

On the Capacity of Noncoherent Network Coding

We consider the problem of multicasting information from a source to a set of receivers over a network where intermediate network nodes perform randomized linear network coding operations on the source packets. We propose a channel model for the noncoherent network coding introduced by Koetter and Kschischang in , that captures the essence of such a network operation, and calculate the capacity as a function of network parameters. We prove that use of subspace coding is optimal, and show that, in some cases, the capacity-achieving distribution uses subspaces of several dimensions, where the employed dimensions depend on the packet length. This model and the results also allow us to give guidelines on when subspace coding is beneficial for the proposed model and by how much, in comparison to a coding vector approach, from a capacity viewpoint. We extend our results to the case of multiple source multicast that creates a virtual multiple access channel.

Graph-constrained group testing

Non-adaptive group testing involves grouping arbitrary subsets of n items into different pools and identifying defective items based on tests obtained for each pool. Motivated by applications in network tomography, sensor networks and infection propagation we formulate non-adaptive group testing problems on graphs. Unlike conventional group testing problems each group here must conform to the constraints imposed by a graph. For instance, items can be associated with vertices and each pool is any set of nodes that must be path connected. In this paper we associate a test with a random walk. In this context conventional group testing corresponds to the special case of a complete graph on n vertices. For interesting classes of graphs we arrive at a rather surprising result, namely, that the number of tests required to identify d defective items is substantially similar to that required in conventional group testing problems, where no such constraints on pooling is imposed. Specifically, if T(n) corresponds to the mixing time of the graph G, we show that with m = O(d2T2(n) log(n/d)) non-adaptive tests, one can identify the defective items. Consequently, for the Erdős-Renyi random graph G(n, p), as well as expander graphs with constant spectral gap, it follows that m = O(d2 log3 n) non-adaptive tests are sufficient to identify d defective items. We next consider a specific scenario that arises in network tomography and show that m = O(d3 log3 n) non-adaptive tests are sufficient to identify d defective items. We also consider noisy counterparts of the graph constrained group testing problem and develop parallel results for these cases.

Approximate capacity of a class of Gaussian relay-interference networks

In this paper we study the Gaussian relay-interference network, in which relay (helper) nodes are to facilitate competing information flows over a wireless network. We examine this problem for certain regimes of channel values, when one of the cross-links is dominated by noise, resulting in Z and/or S configurations for the networks. For these Gaussian ZZ and ZS networks, we establish an approximate characterization of the rate region. The outer bounds to the capacity regions are established using genie-aided techniques that extend the methods used for the Gaussian interference channel to the relay-interference network. For the inner bound of the ZZ network, we utilize a new interference management scheme, termed interference neutralization, which was inspired by our earlier study of such deterministic networks. This technique allows for over-the-air interference removal, without the transmitters having complete access to the interfering signals.