Unitary precoding and basis dependency of MMSE performance for gaussian erasure channels

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buir.contributor.authorHaldun M. Özaktaş
dc.citation.epage7203en_US
dc.citation.issueNumber11en_US
dc.citation.spage7186en_US
dc.citation.volumeNumber60en_US
dc.contributor.authorÖzçelikkale, A.
dc.contributor.authorYüksel S.
dc.contributor.authorÖzaktaş, Haldun M.
dc.date.accessioned2016-02-08T10:59:04Z
dc.date.available2016-02-08T10:59:04Z
dc.date.issued2014en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractWe 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. © 2014 IEEE.en_US
dc.identifier.doi10.1109/TIT.2014.2354034en_US
dc.identifier.issn0018-9448
dc.identifier.urihttp://hdl.handle.net/11693/26384
dc.language.isoEnglishen_US
dc.publisherIEEEen_US
dc.relation.isversionofhttp://dx.doi.org/10.1109/TIT.2014.2354034en_US
dc.source.titleIEEE Transactions on Information Theoryen_US
dc.subjectRandom field estimationen_US
dc.subjectCompressive sensingen_US
dc.subjectErasure channelsen_US
dc.subjectGaussiansen_US
dc.subjectRandom fieldsen_US
dc.subjectUnitary precodingen_US
dc.subjectDiscrete Fourier transformsen_US
dc.titleUnitary precoding and basis dependency of MMSE performance for gaussian erasure channelsen_US
dc.typeArticleen_US
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