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...ance σ 2 s and the measurement noise is assumed to be Gaussian then the lowest bit rate needed to encode ˆsj with a target distortion Dcoded < σ 2 s + σ 2 w/k is given by the rate-distortion function =-=[14]-=- Ro(Dcoded) = 1 2 log¨σ 2 s + σ 2 w/k bits/channel Dcoded © use, (24) where we have implicitly assumed a single channel use for each temporal field sample. It is well-known that for any source with th...

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...sed on piecewise polynomial fits of order ⌈α⌉ − 1. We assume our sensors take samples of the field contaminated by noise. An alternative perspective, that is commonly used in related work [10], [11], =-=[12]-=-, [13], is that f is a realization of a stationary (often bandlimited) random field with some known correlation function. The decay characteristics of the correlation (e.g., the rate of decay) play a ...

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... 2 w. If the destination has direct access to the measurements (noise-free communication), the wellknown (minimax) optimal estimation error is inf £f sup E{�f −¢f� f 2 L2 } ≍ n−2α/(2α+d) in this case =-=[9]-=-. Moreover, a practical field estimator can be easily constructed by partitioning [0, 1] d into m = n d/(2α+d) (square) cells of volume 1/m and computing the least squares fit of an order p = α − 1 po...

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... be based on piecewise polynomial fits of order ⌈α⌉ − 1. We assume our sensors take samples of the field contaminated by noise. An alternative perspective, that is commonly used in related work [10], =-=[11]-=-, [12], [13], is that f is a realization of a stationary (often bandlimited) random field with some known correlation function. The decay characteristics of the correlation (e.g., the rate of decay) p...

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...imation or detection of a single source indicate that joint optimization through a form of source-channel matching, facilitated by limited local node cooperation, can result in dramatic power savings =-=[1]-=-, [2], [3], [4], [5]. In this paper, we propose a distributed architecture for matched source-channel communication for optimized sensing and estimation of a homogeneous spatial field using a wireless...

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...eld estimation is possible as node density increases even if the total network power consumption tends to zero. Our approach involves a novel combination of existing results from approximation theory =-=[6]-=-, statistics [7], and wireless communications [1], [2], [3], [4], [5], [8]. The decay rate of the squared L2-distortion at the destination depends on three quantities; n, the number of wireless sensin...

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...s possible as node density increases even if the total network power consumption tends to zero. Our approach involves a novel combination of existing results from approximation theory [6], statistics =-=[7]-=-, and wireless communications [1], [2], [3], [4], [5], [8]. The decay rate of the squared L2-distortion at the destination depends on three quantities; n, the number of wireless sensing nodes in the n...

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...work power consumption tends to zero. Our approach involves a novel combination of existing results from approximation theory [6], statistics [7], and wireless communications [1], [2], [3], [4], [5], =-=[8]-=-. The decay rate of the squared L2-distortion at the destination depends on three quantities; n, the number of wireless sensing nodes in the network, P , the communication power expended by each node,...

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... would be based on piecewise polynomial fits of order ⌈α⌉ − 1. We assume our sensors take samples of the field contaminated by noise. An alternative perspective, that is commonly used in related work =-=[10]-=-, [11], [12], [13], is that f is a realization of a stationary (often bandlimited) random field with some known correlation function. The decay characteristics of the correlation (e.g., the rate of de...

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...ction of a single source indicate that joint optimization through a form of source-channel matching, facilitated by limited local node cooperation, can result in dramatic power savings [1], [2], [3], =-=[4]-=-, [5]. In this paper, we propose a distributed architecture for matched source-channel communication for optimized sensing and estimation of a homogeneous spatial field using a wireless network of sen...

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... of a single source indicate that joint optimization through a form of source-channel matching, facilitated by limited local node cooperation, can result in dramatic power savings [1], [2], [3], [4], =-=[5]-=-. In this paper, we propose a distributed architecture for matched source-channel communication for optimized sensing and estimation of a homogeneous spatial field using a wireless network of sensors....

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... piecewise polynomial fits of order ⌈α⌉ − 1. We assume our sensors take samples of the field contaminated by noise. An alternative perspective, that is commonly used in related work [10], [11], [12], =-=[13]-=-, is that f is a realization of a stationary (often bandlimited) random field with some known correlation function. The decay characteristics of the correlation (e.g., the rate of decay) play a role a...

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... detection of a single source indicate that joint optimization through a form of source-channel matching, facilitated by limited local node cooperation, can result in dramatic power savings [1], [2], =-=[3]-=-, [4], [5]. In this paper, we propose a distributed architecture for matched source-channel communication for optimized sensing and estimation of a homogeneous spatial field using a wireless network o...