Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimum Pseudo-Weight and Minimum Pseudo-Codewords of LDPC Codes   In this correspondence, we study the minimum pseudo-weight and minimum
pseudo-codewords of low-density parity-check (LDPC) codes under linear
programming (LP) decoding. First, we show that the lower bound of Kelly,
Sridhara, Xu and Rosenthal on the pseudo-weight of a pseudo-codeword of an LDPC
code with girth greater than 4 is tight if and only if this pseudo-codeword is
a real multiple of a codeword. Then, we show that the lower bound of Kashyap
and Vardy on the stopping distance of an LDPC code is also a lower bound on the
pseudo-weight of a pseudo-codeword of this LDPC code with girth 4, and this
lower bound is tight if and only if this pseudo-codeword is a real multiple of
a codeword. Using these results we further show that for some LDPC codes, there
are no other minimum pseudo-codewords except the real multiples of minimum
codewords. This means that the LP decoding for these LDPC codes is
asymptotically optimal in the sense that the ratio of the probabilities of
decoding errors of LP decoding and maximum-likelihood decoding approaches to 1
as the signal-to-noise ratio leads to infinity. Finally, some LDPC codes are
listed to illustrate these results.

33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas