Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: LP/SDP Hierarchy Lower Bounds for Decoding Random LDPC Codes   Random (dv,dc)-regular LDPC codes are well-known to achieve the Shannon
capacity of the binary symmetric channel (for sufficiently large dv and dc)
under exponential time decoding. However, polynomial time algorithms are only
known to correct a much smaller fraction of errors. One of the most powerful
polynomial-time algorithms with a formal analysis is the LP decoding algorithm
of Feldman et al. which is known to correct an Omega(1/dc) fraction of errors.
In this work, we show that fairly powerful extensions of LP decoding, based on
the Sherali-Adams and Lasserre hierarchies, fail to correct much more errors
than the basic LP-decoder. In particular, we show that:
  1) For any values of dv and dc, a linear number of rounds of the
Sherali-Adams LP hierarchy cannot correct more than an O(1/dc) fraction of
errors on a random (dv,dc)-regular LDPC code.
  2) For any value of dv and infinitely many values of dc, a linear number of
rounds of the Lasserre SDP hierarchy cannot correct more than an O(1/dc)
fraction of errors on a random (dv,dc)-regular LDPC code.
  Our proofs use a new stretching and collapsing technique that allows us to
leverage recent progress in the study of the limitations of LP/SDP hierarchies
for Maximum Constraint Satisfaction Problems (Max-CSPs). The problem then
reduces to the construction of special balanced pairwise independent
distributions for Sherali-Adams and special cosets of balanced pairwise
independent subgroups for Lasserre.
  Some of our techniques are more generally applicable to a large class of
Boolean CSPs called Min-Ones. In particular, for k-Hypergraph Vertex Cover, we
obtain an improved integrality gap of $k-1-\epsilon$ that holds after a
\emph{linear} number of rounds of the Lasserre hierarchy, for any k = q+1 with
q an arbitrary prime power. The best previous gap for a linear number of rounds
was equal to $2-\epsilon$ and due to Schoenebeck.

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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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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: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: eess