Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Cages to Trapping Sets and Codewords: A Technique to Derive Tight
  Upper Bounds on the Minimum Size of Trapping Sets and Minimum Distance of
  LDPC Codes   Cages, defined as regular graphs with minimum number of nodes for a given
girth, are well-studied in graph theory. Trapping sets are graphical structures
responsible for error floor of low-density parity-check (LDPC) codes, and are
well investigated in coding theory. In this paper, we make connections between
cages and trapping sets. In particular, starting from a cage (or a modified
cage), we construct a trapping set in multiple steps. Based on the connection
between cages and trapping sets, we then use the available results in graph
theory on cages and derive tight upper bounds on the size of the smallest
trapping sets for variable-regular LDPC codes with a given variable degree and
girth. The derived upper bounds in many cases meet the best known lower bounds
and thus provide the actual size of the smallest trapping sets. Considering
that non-zero codewords are a special case of trapping sets, we also derive
tight upper bounds on the minimum weight of such codewords, i.e., the minimum
distance, of variable-regular LDPC codes as a function of variable degree and
girth.

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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: nlin
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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-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex