Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Error Exponent of Approximate Sufficient Statistics for M-ary
  Hypothesis Testing   Consider the problem of detecting one of M i.i.d. Gaussian signals corrupted
in white Gaussian noise. Conventionally, matched filters are used for
detection. We first show that the outputs of the matched filter form a set of
asymptotically optimal sufficient statistics in the sense of maximizing the
error exponent of detecting the true signal. In practice, however, M may be
large which motivates the design and analysis of a reduced set of N statistics
which we term approximate sufficient statistics. Our construction of these
statistics is based on a small set of filters that project the outputs of the
matched filters onto a lower-dimensional vector using a sensing matrix. We
consider a sequence of sensing matrices that has the desiderata of row
orthonormality and low coherence. We analyze the performance of the resulting
maximum likelihood (ML) detector, which leads to an achievable bound on the
error exponent based on the approximate sufficient statistics; this bound
recovers the original error exponent when N = M. We compare this to a bound
that we obtain by analyzing a modified form of the Reduced Dimensionality
Detector (RDD) proposed by Xie, Eldar, and Goldsmith [IEEE Trans. on Inform.
Th., 59(6):3858-3874, 2013]. We show that by setting the sensing matrices to be
column-normalized group Hadamard matrices, the exponents derived are
ensemble-tight, i.e., our analysis is tight on the exponential scale given the
sensing matrices and the decoding rule. Finally, we derive some properties of
the exponents, showing, in particular, that they increase linearly in the
compression ratio N/M.

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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas