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**Harvard**

Ozcelikkale, A., Yuksel, S. och Ozaktas, H. (2014) *Unitary Precoding and Basis Dependency of MMSE Performance for Gaussian Erasure Channels*.

** BibTeX **

@article{

Ozcelikkale2014,

author={Ozcelikkale, Ayca and Yuksel, S. and Ozaktas, H. M.},

title={Unitary Precoding and Basis Dependency of MMSE Performance for Gaussian Erasure Channels},

journal={IEEE Transactions on Information Theory},

issn={0018-9448},

volume={60},

issue={11},

pages={7186-7203},

abstract={We consider the transmission of a Gaussian vector source over a multidimensional Gaussian channel where a random or a fixed subset of the channel outputs are erased. Within the setup where the only encoding operation allowed is a linear unitary transformation on the source, we investigate the minimum mean-square error (MMSE) performance, both in average, and also in terms of guarantees that hold with high probability as a function of the system parameters. Under the performance criterion of average MMSE, necessary conditions that should be satisfied by the optimal unitary encoders are established and explicit solutions for a class of settings are presented. For random sampling of signals that have a low number of degrees of freedom, we present MMSE bounds that hold with high probability. Our results illustrate how the spread of the eigenvalue distribution and the unitary transformation contribute to these performance guarantees. The performance of the discrete Fourier transform (DFT) is also investigated. As a benchmark, we investigate the equidistant sampling of circularly wide-sense stationary signals, and present the explicit error expression that quantifies the effects of the sampling rate and the eigenvalue distribution of the covariance matrix of the signal. These findings may be useful in understanding the geometric dependence of signal uncertainty in a stochastic process. In particular, unlike information theoretic measures such as entropy, we highlight the basis dependence of uncertainty in a signal with another perspective. The unitary encoding space restriction exhibits the most and least favorable signal bases for estimation.},

year={2014},

keywords={Random field estimation, compressive sensing, discrete fourier transform},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 208231

A1 Ozcelikkale, Ayca

A1 Yuksel, S.

A1 Ozaktas, H. M.

T1 Unitary Precoding and Basis Dependency of MMSE Performance for Gaussian Erasure Channels

YR 2014

JF IEEE Transactions on Information Theory

SN 0018-9448

VO 60

IS 11

SP 7186

OP 7203

AB We consider the transmission of a Gaussian vector source over a multidimensional Gaussian channel where a random or a fixed subset of the channel outputs are erased. Within the setup where the only encoding operation allowed is a linear unitary transformation on the source, we investigate the minimum mean-square error (MMSE) performance, both in average, and also in terms of guarantees that hold with high probability as a function of the system parameters. Under the performance criterion of average MMSE, necessary conditions that should be satisfied by the optimal unitary encoders are established and explicit solutions for a class of settings are presented. For random sampling of signals that have a low number of degrees of freedom, we present MMSE bounds that hold with high probability. Our results illustrate how the spread of the eigenvalue distribution and the unitary transformation contribute to these performance guarantees. The performance of the discrete Fourier transform (DFT) is also investigated. As a benchmark, we investigate the equidistant sampling of circularly wide-sense stationary signals, and present the explicit error expression that quantifies the effects of the sampling rate and the eigenvalue distribution of the covariance matrix of the signal. These findings may be useful in understanding the geometric dependence of signal uncertainty in a stochastic process. In particular, unlike information theoretic measures such as entropy, we highlight the basis dependence of uncertainty in a signal with another perspective. The unitary encoding space restriction exhibits the most and least favorable signal bases for estimation.

LA eng

DO 10.1109/tit.2014.2354034

LK http://dx.doi.org/10.1109/tit.2014.2354034

LK http://publications.lib.chalmers.se/records/fulltext/208231/local_208231.pdf

OL 30