Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes   In this work, we consider pseudocodewords of (relaxed) linear programming
(LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP
decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo
codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is
proper and $C$-symmetric, and make a connection to finite graph covers of the
3D-TC factor graph. This connection is used to show that the support set of any
pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum
a posteriori constituent decoders on the binary erasure channel. Furthermore,
we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a
finite-length minimum pseudoweight analysis for small cover degrees. Also, an
explicit description of the fundamental cone of the 3D-TC polytope is given.
Finally, we present an extensive numerical study of small-to-medium block
length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the
minimum distance $d_{\rm min}$ and/or the stopping distance $h_{\rm min}$ is
high, the minimum pseudoweight (on the additive white Gaussian noise channel)
is strictly smaller than both the $d_{\rm min}$ and the $h_{\rm min}$, and 2)
the minimum pseudoweight grows with the block length, at least for
small-to-medium block lengths.

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The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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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: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th