Nomographic Functions: Efficient Computation in Clustered Gaussian Sensor Networks

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.Comment: to appear in IEEE Transactions on Wireless Communication

Exploiting Interference for Efficient Distributed Computation in Cluster-based Wireless Sensor Networks

This invited paper presents some novel ideas on how to enhance the performance of consensus algorithms in distributed wireless sensor networks, when communication costs are considered. Of particular interest are consensus algorithms that exploit the broadcast property of the wireless channel to boost the performance in terms of convergence speeds. To this end, we propose a novel clustering based consensus algorithm that exploits interference for computation, while reducing the energy consumption in the network. The resulting optimization problem is a semidefinite program, which can be solved offline prior to system startup.Comment: Accepted for publication at IEEE Global Conference on Signal and Information Processing (GlobalSIP 2013

A Dimensionality Reduction Method for Finding Least Favorable Priors with a Focus on Bregman Divergence

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.8080809415

Amplitude Constrained MIMO Channels: Properties of Optimal Input Distributions and Bounds on the Capacity

In this work, the capacity of multiple-input multiple-output channels that are subject to constraints on the support of the input is studied. The paper consists of two parts. The first part focuses on the general structure of capacity-achieving input distributions. Known results are surveyed and several new results are provided. With regard to the latter, it is shown that the support of a capacity-achieving input distribution is a small set in both a topological and a measure theoretical sense. Moreover, explicit conditions on the channel input space and the channel matrix are found such that the support of a capacity-achieving input distribution is concentrated on the boundary of the input space only. The second part of this paper surveys known bounds on the capacity and provides several novel upper and lower bounds for channels with arbitrary constraints on the support of the channel input symbols. As an immediate practical application, the special case of multiple-input multiple-output channels with amplitude constraints is considered. The bounds are shown to be within a constant gap to the capacity if the channel matrix is invertible and are tight in the high amplitude regime for arbitrary channel matrices. Moreover, in the regime of high amplitudes, it is shown that the capacity scales linearly with the minimum between the number of transmit and receive antennas, similar to the case of average power-constrained inputs

Amplitude Constrained MIMO Channels: Properties of Optimal Input Distributions and Bounds on the Capacity

Entropy 2019, 21(2), 20