Lossy network correlated data gathering with high-resolution coding

Sensor networks measuring correlated data are considered, where the task is to gather data from the network nodes to a sink. A specific scenario is addressed, where data at nodes are lossy coded with high-resolution, and the information measured by the nodes has to be reconstructed at the sink within both certain total and individual distortion bounds. The first problem considered is to find the optimal transmission structure and the rate-distortion allocations at the various spatially located nodes, such as to minimize the total power consumption cost of the network, by assuming fixed nodes positions. The optimal transmission structure is the shortest path tree and the problems of rate and distortion allocation separate in the high-resolution case, namely, first the distortion allocation is found as a function of the transmission structure, and second, for a given distortion allocation, the rate allocation is computed. The second problem addressed is the case when the node positions can be chosen, by finding the optimal node placement for two different targets of interest, namely total power minimization and network lifetime maximization. Finally, a node placement solution that provides a tradeoff between the two metrics is proposed

An Optimal Medium Access Control with Partial Observations for Sensor Networks

We consider medium access control (MAC) in multihop sensor networks, where only partial information about the shared medium is available to the transmitter. We model our setting as a queuing problem in which the service rate of a queue is a function of a partially observed Markov chain representing the available bandwidth, and in which the arrivals are controlled based on the partial observations so as to keep the system in a desirable mildly unstable regime. The optimal controller for this problem satisfies a separation property: we first compute a probability measure on the state space of the chain, namely the information state, then use this measure as the new state on which the control decisions are based. We give a formal description of the system considered and of its dynamics, we formalize and solve an optimal control problem, and we show numerical simulations to illustrate with concrete examples properties of the optimal control law. We show how the ergodic behavior of our queuing model is characterized by an invariant measure over all possible information states, and we construct that measure. Our results can be specifically applied for designing efficient and stable algorithms for medium access control in multiple-accessed systems, in particular for sensor networks

Networked Slepian-Wolf: theory, algorithms, and scaling laws

Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the data-gathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by Slepian-Wolf coding. The overall minimization can be achieved in two concatenated steps. First, the optimal transmission structure is found, which in general amounts to finding a Steiner tree, and second, the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure, and with linear constraints given by the Slepian-Wolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closed-form solution for the optimal rate allocation is provided. For the general case of an arbitrary traffic matrix, the problem of finding the optimal transmission structure is NP-complete. For large networks, in some simplified scenarios, the total costs associated with Slepian-Wolf coding and explicit communication (conditional encoding based on explicitly communicated side information) are compared. Finally, the design of decentralized algorithms for the optimal rate allocation is analyzed

Adaptive distributed algorithms for power-efficient data gathering in sensor networks

In this work, we consider the problem of designing adaptive distributed processing algorithms in large sensor networks that are efficient in terms of minimizing the total power spent for gathering the spatially correlated data from the sensor nodes to a sink node. We take into account both the power spent for purposes of communication as well as the power spent for local computation. Our distributed algorithms are also matched to the nature of the correlated field, namely, for piecewise smooth signals, we provide two distributed multiresolution wavelet-based algorithms, while for correlated Gaussian fields, we use distributed prediction based processing. In both cases, we provide distributed algorithms that perform network division into groups of different sizes. The distribution of the group sizes within the network is the result of an optimal trade-off between the local communication inside each group needed to perform decorrelation, the communication needed to bring the processed data (coefficients) to the sink and the local computation cost, which grows as the network becomes larger. Our experimental results show clearly that important gains in power consumption can be obtained with respect to the case of not performing any distributed decorrelating processing

On the optimal density for real-time data gathering of spatio-temporal processes in sensor networks

Abstract — We consider sensor networks that measure spatio-temporal correlated processes. An important task in such settings is the reconstruction at a certain node, called the sink, of the data at all points of the field. We consider scenarios where data is time critical, so delay results in distortion, or suboptimal estimation and control. For the reconstruction, the only data available to the sink are the values measured at the nodes of the sensor network, and knowledge of the correlation structure: this results in spatial distortion of reconstruction. Also, for the sake of power efficiency, sensor nodes need to transmit their data by relaying through the other network nodes: this results in delay, and thus temporal distortion of reconstruction if time critical data is concerned. We study data gathering for the case of Gaussian processes in one- and twodimensional grid scenarios, where we are able to write explicit expressions for the spatial and time distortion, and combine them into a single total distortion measure. We prove that, for various standard correlation structures, there is an optimal finite density of the sensor network for which the total distortion is minimized. Thus, when power efficiency and delay are both considered in data gathering, it is useless from the point of view of accuracy of the reconstruction to increase the number of sensors above a certain threshold that depends on the correlation structure characteristics

On the optimal density for real-time data gathering of spatio-temporal processes in sensor networks

Abstract — We consider sensor networks that measure spatio-temporal correlated processes. An important task in such settings is the reconstruction at a certain node, called the sink, of the data at all points of the field. We consider scenarios where data is time critical, so delay results in distortion, or suboptimal estimation and control. For the reconstruction, the only data available to the sink are the values measured at the nodes of the sensor network, and knowledge of the correlation structure: this results in spatial distortion of reconstruction. Also, for the sake of power efficiency, sensor nodes need to transmit their data by relaying through the other network nodes: this results in delay, and thus temporal distortion of reconstruction if time critical data is concerned. We study data gathering for the case of Gaussian processes in one- and twodimensional grid scenarios, where we are able to write explicit expressions for the spatial and time distortion, and combine them into a single total distortion measure. We prove that, for various standard correlation structures, there is an optimal finite density of the sensor network for which the total distortion is minimized. Thus, when power efficiency and delay are both considered in data gathering, it is useless from the point of view of accuracy of the reconstruction to increase the number of sensors above a certain threshold that depends on the correlation structure characteristics

Power-efficient sensor placement and transmission structure for data gathering under distortion constraints

We consider the joint optimization of sensor placement and transmission structure for data gathering, where a given number of nodes need to be placed in a field such that the sensed data can be reconstructed at a sink within specified distortion bounds while minimizing the energy consumed for communication. We assume that the nodes use either joint entropy coding based on explicit communication between sensor nodes, where coding is done when side information is available, or Slepian-Wolf coding where nodes have knowledge of network correlation statistics. We consider both maximum and average distortion bounds. We prove that this optimization is NP-complete since it involves an interplay between the spaces of possible transmission structures given radio reachability limitations, and feasible placements satisfying distortion bounds. We address this problem by first looking at the simplified problem of optimal placement in the one-dimensional case. An analytical solution is derived for the case when there is a simple aggregation scheme, and numerical results are provided for the cases when joint entropy encoding is used. We use the insight from our 1-D analysis to extend our results to the 2-D case and compare it to typical uniform random placement and shortest-path tree. Our algorithm for two-dimensional placement and transmission structure provides two to three fold reduction i

Joint source-channel coding . . .

We consider the interaction between the physical representation of information in a correlated data field, and the way that information is transmitted to a central processor. Namely, we study data gathering to a sink node, by considering a set of relevant metrics: first we consider energy efficiency, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node, and second we consider mean-square-error (MSE) distortion, where the goal is to represent the information field with a maximal accuracy. The first problem requires a joint optimization of the data representation at the nodes and of the transmission structure; we study both the lossless scenario with Slepian-Wolf coding, and the high-resolution lossy scenario with optimal rate-distortion allocation. We show that the optimal transmission structure is the shortest path tree, and we find in closed-form the rate and distortion allocation. The second problem is relevant for data gathering of spatio-temporal correlated processes under delay constraints, where we show that both the temporal and the spatial distortion can be combined in a single measure of distortion, which depends on the density of the network. We prove that, for various standard correlation structures, there is an optimal finite densit