Title
Nomographic Functions: Efficient Computation in Clustered Gaussian Sensor Networks
Abstract
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.
Year
DOI
Venue
2015
10.1109/TWC.2014.2380317
Wireless Communications, IEEE Transactions  
Keywords
Field
DocType
Gaussian channels,nonlinear functions,radiofrequency interference,sensor fusion,wireless sensor networks,Gaussian multipleaccess channels,channel noise,clustered Gaussian sensor networks,clustered wireless sensor network,fusion centers,lattice code design,nomographic functions,preprocessed sensor readings,In-network computation,Kolmogorov’s superpositions,Kolmogorov's superpositions,multiple-access channel,multipleaccess channel,nested lattice codes,nomographic functions,wireless sensor networks
Key distribution in wireless sensor networks,Continuous function,Algorithm,Real-time computing,Theoretical computer science,Gaussian,Interference (wave propagation),Mobile wireless sensor network,Decoding methods,Wireless sensor network,Mathematics,Computation
Journal
Volume
Issue
ISSN
14
4
1536-1276
Citations 
PageRank 
References 
12
0.58
17
Authors
3
Name
Order
Citations
PageRank
Mario Goldenbaum113513.40
Holger Boche22348265.41
Slawomir Stanczak352189.71