Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical lower bounds for the size of elementary trapping sets of
  variable-regular LDPC codes with any girth and irregular ones with girth 8   In this paper we give lower bounds on the size of $(a,b)$ elementary trapping
sets (ETSs) belonging to variable-regular LDPC codes with any girth, $g$, and
irregular ones with girth 8, where $a$ is the size, $b$ is the number of
degree-one check nodes and satisfy the inequality $\frac{b}{a}<1$. Our proposed
lower bounds are analytical, rather than exhaustive search-based, and based on
graph theories. The numerical results in the literarture for $g=6,8$ for
variable-regular LDPC codes match our results. Some of our investigations are
independent of the girth and rely on the variables $a$, $b$ and $\gamma$, the
column weight value, only. We prove that for an ETS belonging to a
variable-regular LDPC code with girth 8 we have $a\geq2\gamma-1$ and
$b\geq\gamma$. We demonstrate that these lower bounds are tight, making use of
them we provide a method to achieve the minimum size of ETSs belonging to
irregular LDPC codes with girth 8 specially those whose column weight values
are a subset of $\{2,3,4,5,6\}$. Moreover, we show for variable-regular LDPC
codes with girth 10, $a\geq(\gamma-1)^2+1$. And for $\gamma=3,4$ we obtain
$a\geq7$ and $a\geq12$, respectively. Finally, for variable-regular LDPC codes
with girths $g=2(2k+1)$ and $g=2(2k+2)$ we obtain $a\geq(\gamma-2)^k+1$ and
$a\geq2(\gamma-2)^k+1$, respectively.

37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int