Does analog transmission achieve OPTA in an asymmetric Gaussian sensor network ?

We consider the estimation of a Gaussian source by a Gaussian sensor network where L distributed sensors transmit noisy observations of the source through a Gaussian multiple access channel to a fusion center. In a recent work, Gastpar showed that for a symmetric sensor network with no fading, analog (uncoded) transmission achieves the optimal performance theoretically attainable (OPTA). In this work, by comparing lower and upper bounds on the OPTA, we provide optimality conditions for analog transmission in an asymmetric Gaussian sensor network with deterministic fading. We also obtain an optimal power allocation scheme to minimize the mean-squared error distortion given a linear combination of powers (LCP) constraint. We determine optimality conditions for analog transmission under an LCP constraint, which includes the sum-power constraint as a special case.

[1]  Michael Gastpar,et al.  Power, spatio-temporal bandwidth, and distortion in large sensor networks , 2005, IEEE Journal on Selected Areas in Communications.

[2]  Amos Lapidoth,et al.  Sending a Bi-Variate Gaussian Source over a Gaussian MAC , 2006, 2006 IEEE International Symposium on Information Theory.

[3]  Amos Lapidoth,et al.  Sending a Bivariate Gaussian Over a Gaussian MAC , 2010, IEEE Transactions on Information Theory.

[4]  Vinod Sharma,et al.  Source-channel coding for Gaussian sources over a Gaussian multiple access channel , 2007 .

[5]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[6]  Z.-Q. Luo,et al.  Power-efficient analog forwarding transmission in an inhomogeneous Gaussian sensor network , 2005, IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, 2005..

[7]  M. Reza Soleymani,et al.  On the optimal power-distortion tradeoff in asymmetric gaussian sensor network , 2009, IEEE Transactions on Communications.

[8]  Thomas J. Goblick,et al.  Theoretical limitations on the transmission of data from analog sources , 1965, IEEE Trans. Inf. Theory.

[9]  Amos Lapidoth,et al.  Broadcasting Correlated Gaussians , 2007, IEEE Transactions on Information Theory.

[10]  Michael Gastpar,et al.  To code, or not to code: lossy source-channel communication revisited , 2003, IEEE Trans. Inf. Theory.

[11]  R. Rajesh,et al.  A joint source-channel coding scheme for transmission of correlated discrete sources over a Gaussian Multiple Access Channel , 2008, 2008 International Symposium on Information Theory and Its Applications.

[12]  Michael Gastpar,et al.  Uncoded transmission is exactly optimal for a simple Gaussian "sensor" network , 2008, 2007 Information Theory and Applications Workshop.

[13]  H. Witsenhausen.  ON SEQUENCES OF PAIRS OF DEPENDENT RANDOM VARIABLES , 1975 .

[14]  Fady Alajaji,et al.  On the optimal power-distortion region for asymmetric Gaussian sensor networks with fading , 2008, 2008 IEEE International Symposium on Information Theory.