Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-SNR Asymptotics of Mutual Information for Discrete Constellations
  with Applications to BICM   Asymptotic expressions of the mutual information between any discrete input
and the corresponding output of the scalar additive white Gaussian noise
channel are presented in the limit as the signal-to-noise ratio (SNR) tends to
infinity. Asymptotic expressions of the symbol-error probability (SEP) and the
minimum mean-square error (MMSE) achieved by estimating the channel input given
the channel output are also developed. It is shown that for any input
distribution, the conditional entropy of the channel input given the output,
MMSE and SEP have an asymptotic behavior proportional to the Gaussian
Q-function. The argument of the Q-function depends only on the minimum
Euclidean distance (MED) of the constellation and the SNR, and the
proportionality constants are functions of the MED and the probabilities of the
pairs of constellation points at MED. The developed expressions are then
generalized to study the high-SNR behavior of the generalized mutual
information (GMI) for bit-interleaved coded modulation (BICM). By means of
these asymptotic expressions, the long-standing conjecture that Gray codes are
the binary labelings that maximize the BICM-GMI at high SNR is proven. It is
further shown that for any equally spaced constellation whose size is a power
of two, there always exists an anti-Gray code giving the lowest BICM-GMI at
high SNR.

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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: gr-qc