Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unitary Precoding and Basis Dependency of MMSE Performance for Gaussian
  Erasure Channels   We consider the transmission of a Gaussian vector source over a
multi-dimensional 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
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 (c.w.s.s.) 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.

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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org