A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior, under mild conditions, is then known to be minimax. However, finding least favorable distributions can be challenging due to inherent optimization over the space of probability distributions, which is infinite-dimensional. This paper develops a dimensionality reduction method that allows us to move the optimization to a finite-dimensional setting with an explicit bound on the dimension. The benefit of this dimensionality reduction is that it permits the use of popular algorithms such as projected gradient ascent to find least favorable priors. Throughout the paper, in order to make progress on the problem, we restrict ourselves to Bayesian risks induced by a relatively large class of loss functions, namely Bregman divergences.

In this work, novel upper and lower bounds on the capacity of channels with arbitrary constraints on the support of the channel input symbols are derived. As an immediate practical application, the case of multiple-input multiple- output channels with amplitude constraints is considered. The bounds are shown to be within a constant gap if the channel matrix is invertible and are tight in the high amplitude regime for arbitrary channel matrices. Moreover, in the high amplitude regime, it is shown that the capacity scales linearly with the minimum of the numbers of transmit and receive antennas, similarly to the case of average power-constrained inputs.

In this paper, a generalized Ozarow-Wyner capacity bound is presented that holds for arbitrary noise channels. The bound is then used to approximate the capacity of a large class of additive noise channels that are subject to a p-th moment input constraint, where p is some positive real number, as well as to the Cauchy noise channel with a logarithmic moment constraint. For both channel models the gap to the capacity is precisely specified.

In this paper, the problem of simultaneously generating multiple keys over a cascade of a noiseless channel and a wiretap channel is considered. The problem consists of three legitimate parties (i.e., Alice, Bob, and Carol) and an eavesdropper (Eve), where Alice and Bob wish to agree with Carol on independent secret keys, both of which should be kept secret from Eve. Alice and Bob are connected via a noiseless channel, and Bob is connected with Carol via a wiretap channel, while there is no direct connection between Alice and Carol. To Alice and Carol, Bob acts as a relay. Under this model, a full characterization of the secret-key capacity region is provided for the case in which Eve has no side information. This result shows that there exists a tradeoff between the individual secret-key rates. Then, this result is generalized to the case in which Eve has side information, and the corresponding secret-key capacity region is fully characterized.

Anomaly detection has various applications including condition monitoring and fault diagnosis. The objective is to sense the environment, learn the normal system state, and then periodically classify whether the instantaneous state deviates from the normal one or not. Wireless sensor networks provide a flexible and cost-effective way of monitoring a system state. In traditional wireless sensor networks, sensors encode their observations and transmit them to a fusion center using some interference avoiding channel access method. The fusion center decodes all the data and then classifies the corresponding system state. As this approach is in general highly inefficient, this paper proposes a transmission scheme that, instead of avoiding the interference, exploits it for carrying out the anomaly detection directly in the air. In other words, the wireless channel helps the fusion center to retrieve the sought classification outcome immediately from the channel output. To achieve this, the chosen learning model is a linear support vector machine. After proving the reliability of the proposed scheme, numerical examples are presented that demonstrate its ability to reduce the energy consumption for anomaly detection by up to 53 % compared to a strategy that uses time division multiple-access.

In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matches the algebraic structure of the channel and the joint source distribution fulfills certain conditions, the secrecy computation-capacity equals the computation capacity, which is the supremum of all achievable computation rates without secrecy constraints. Unlike the case of securely transmitting messages, no additional randomness is needed at the encoders nor does the legitimate receiver need any advantage over the eavesdropper. The results therefore show that the problem of securely computing a function over a multiple-access wiretap channel may significantly differ from the one of securely communicating messages.

In this paper, the problem of simultaneously generating multiple keys over a cascade of a noiseless channel and a wiretap channel is considered. The problem consists of three legitimate parties, i.e., Alice, Bob and Carol, where Alice and Bob wish to agree with Carol on independent secret keys. Alice and Bob are connected via a noiseless channel, and Bob is connected with Carol via a wiretap channel, while there is no direct connection between Alice and Carol. To Alice and Carol, Bob acts as a relay. Under this model, a single-letter characterization of the secret-key capacity region is provided. The result shows that there exists a trade-off between the individual secret-key rates.

In this work, a recently proposed analog transmission scheme is considered, which harnesses interference for reliably and efficiently computing real-valued functions over a wireless channel. To better understand the corresponding trade-off between the conflicting demands of reliability and efficiency, in this paper we choose an information theoretic perspective by analyzing the scheme within the framework of computation coding. Towards this end, we first adapt the standard notions of a computation code and an achievable computation rate to our specific needs and then provide rate expressions for some simple but insightful examples. It turns out that the achievable computation rates not only depend on the function to be computed but also on the desired accuracy and the number of concurrently active transmitters.

In this paper, a clustered wireless sensor network is considered that is modeled as a set of coupled Gaussian multiple-access channels. The objective of the network is not to reconstruct individual sensor readings at designated fusion centers but rather to reliably compute some functions thereof. Our particular attention is on real-valued functions that can be represented as a post-processed sum of pre-processed sensor readings. Such functions are called nomographic functions and their special structure permits the utilization of the interference property of the Gaussian multiple-access channel to reliably compute many linear and nonlinear functions at significantly higher rates than those achievable with standard schemes that combat interference. Motivated by this observation, a computation scheme is proposed that combines a suitable data pre- and post-processing strategy with a nested lattice code designed to protect the sum of pre-processed sensor readings against the channel noise. After analyzing its computation rate performance, it is shown that at the cost of a reduced rate, the scheme can be extended to compute every continuous function of the sensor readings in a finite succession of steps, where in each step a different nomographic function is computed. This demonstrates the fundamental role of nomographic representations.

In this paper, a wireless sensor network is considered in which the objective is not to communicate individual sensor readings over a Gaussian multiple-access channel to a fusion center but rather to reliably compute some nomographic function thereof. Nomographic functions are exactly those multivariate functions that can be represented as a post-processed sum of pre-processed sensor readings. This special structure permits the utilization of the interference property of the Gaussian multiple-access channel for computing some nomographic functions at significantly higher rates than those achievable with traditional schemes. In this paper, a corresponding coding scheme is presented that protects the sum of pre-processed sensor readings against the channel noise by letting each node use the same nested lattice code.

Wireless sensor network applications often involve the computation of pre-defined functions of the measurements such as for example the arithmetic mean or maximum value. Standard approaches to this problem separate communication from computation: digitized sensor readings are transmitted interference-free to a fusion center that reconstructs each sensor reading and subsequently computes the sought function value. Such separation-based computation schemes are generally highly inefficient as a complete reconstruction of individual sensor readings at the fusion center is not necessary to compute a function of them. In particular, if the mathematical structure of the channel is suitably matched (in some sense) to the function of interest, then channel collisions induced by concurrent transmissions of different nodes can be beneficially exploited for computation purposes. This paper proposes an analog computation scheme that allows for an efficient estimate of linear and nonlinear functions over the wireless multiple-access channel. A match between the channel and the function being evaluated is thereby achieved via some pre-processing on the sensor readings and post-processing on the superimposed signals observed by the fusion center. After analyzing the estimation error for two function examples, simulations are presented to show the potential for huge performance gains over time- and code-division multiple-access based computation schemes.

Recently, it has been shown that the superposition property of wireless multiple-access channels can be exploited to compute functions in sensor networks much more efficiently. By using appropriate pre- and post-processing functions operating on real sensor readings and the superimposed signal received by a fusion center, every function of the measurements is in principle computable by means of the wireless channel in which the pre-processing functions, and therefore the transmitting nodes, do not depend on the function of interest. In this paper we extend these general considerations by examining how robust this kind of universality is against variations in network topology due to nodes that drop out of the network or due to new nodes that connect to the network.

In this paper we propose a gossip algorithm for average consensus in clustered wireless sensor networks called superposition gossiping, where the nodes in each cluster exploit the natural superposition property of wireless multiple-access channels to significantly decrease local averaging times. More precisely, the considered network is organized into single-hop clusters and in each cluster average values are computed at a designated cluster head via the wireless channel and subsequently broadcasted to update the entire cluster. Since the clusters are activated randomly in a time division multiple-access fashion, we can apply well-established techniques for analyzing gossip algorithms to prove the convergence of the algorithm to the average consensus in the second moment and almost surely, provided that some connectivity condition between clusters is fulfilled. Finally, we follow a semidefinite programming approach to optimize wake up probabilities of cluster heads that further accelerates convergence.

We consider a power-controlled wireless network with an established network topology in which the communication links (transmitter-receiver pairs) are subject to general constraints on transmit powers and corrupted by the co-channel interference and background noise. In this paper, we characterize the max-min SIR power allocation and provide a saddle point characterization of this power allocation under weaker conditions. This characterization is a basis for novel algorithms for computing a max-min SIR power allocation.

We view a wireless sensor network as a collection of sensor nodes that observe sources of information, process the picked up data and send it to a sink node, with the goal of computing a desired function of the measurements. To this end, we consider a previously proposed coding scheme that exploits the underlying fading multiple-access channel (MAC) to efficiently estimate the function values. The main problem addressed in this paper is how much channel state information (CSI) is needed at the sensor nodes to obtain sufficiently good estimates? First we show that there is no performance loss, independent of fading distributions, if, instead of perfect CSI, each sensor node has only access to the modulus of its channel coefficient. In the case of multiple antenna elements at the sink node and specific independent distributed fading environments, it is shown that CSI at sensor nodes is not necessary and a very simple correction of fading effects can be performed at the sink based on some statistical channel knowledge. In many cases, fading improves the estimation accuracy due to the multiple-access nature of the channel.

In wireless sensor networks, the identity of a particular sensor node and a complete reconstruction of sensed data at a designated sink node may be not needed. Indeed, the objective is often to compute a certain function of the sensed data. Such desired functions can be for example the arithmetic mean, the geometric mean, polynomials and other functions that adequately match the mathematical characteristic of the underlying multiple-access channel. In this paper, we propose a simple practical approach to compute desired functions of sensor network data, exploiting explicitly the mathematical characteristic of the wireless sensor multiple-access channel (WS-MAC). In contrast to traditional schemes that are designed to combat interference caused by other connections, we exploit this interference with the goal of computing the desired functions, which is in a sense a paradigm shift. This leads directly to a higher data rate in terms of function computation or a higher SNR in comparison to other schemes like time division multiple access (TDMA). Our approach needs no extensive symbol or phase synchronization, since the measured values are converted into the transmit power of a specific random transmit sequence with unit norm. Only a coarse block synchronization is necessary so that the proposed scheme is easy to implement.