Codes for Sensors: An Algorithmic Perspective

Abstract

Sensing, processing and transmitting data are arguably the key activities of common nodes in a wireless sensor network once embedded in a physical process unfolding in time and space. To process the data and transmit it reliably and efficiently over noisy links along the network, sensor nodes require codes that are capable of exploiting the natural correlation of the gathered data and of combating the impairments caused by noisy communication channels.

Once we define reasonable models for the information sources and the communication channels, information theory offers powerful tools to study the ultimate performance limits for any coding scheme designed for this class of communication and computation systems. To illustrate this observation, we start by modeling the sensor network as a set of multiple correlated sources that are observed by partially cooperating encoders and transmitted over a network of independent channels. Based on this formulation, we are able to characterize the network capacity, i.e., the exact conditions on the sources and the channels under which there exist codes for reliable communication with the data collection point. An important conclusion to be drawn from our proofs, is that for a large (and arguably most relevant) class of sensor networks, separate data compression and error correction codes provide an optimal system architecture.

The proofs also offer hints on how to construct practical algorithms for distributed compression and joint inference of correlated data collected by hundreds of sensor nodes. After showing that the optimal decoder based on minimum mean square estimation (MMSE) is unfeasible – its complexity grows exponentially with the number of nodes – we present a two-step “scalable” alternative: (1) approximate the correlation structure of the data with a suitable factor-graph, and (2) perform joint source/channel decoding on this graph using the sum-product algorithm. Based on this general approach, which can be applied to sensor networks with arbitrary topologies, we give an exact characterization of the decoding complexity, as well as optimization algorithms for finding optimal factor trees under the Kulback-Leibler criterion. Finally, we are able to show how these ideas can also be used for distortion-optimized index assignments for low-complexity distributed quantization, and source-optimized hierarchical clustering.

Keynote speech.