Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical Bounds on Maximum-Likelihood Decoded Linear Codes with
  Applications to Turbo-Like Codes: An Overview   Upper and lower bounds on the error probability of linear codes under
maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles
of codes on graphs. For upper bounds, focus is put on Gallager bounding
techniques and their relation to a variety of other reported bounds. Within the
class of lower bounds, we address de Caen's based bounds and their
improvements, sphere-packing bounds, and information-theoretic bounds on the
bit error probability of codes defined on graphs. A comprehensive overview is
provided in a monograph by the authors which is currently in preparation.

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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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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: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: alg-geom