Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Analysis of Puncturing for Finite-Length Polar Codes: Boolean
  Function Approach   This paper investigates the impact of puncturing on finite-length polar codes
in which a puncturing pattern $\pv^{N}=(p_0,...,p_N)$ is applied to a
length-$N$ polar code.. We first introduce two virtual channels to
stochastically model the punctured (untransmitted) bits, which are respectively
called {\em useless channel model} (UCM) and {\em deterministic channel model}
(DCM). Under each model, we derive boolean functions in variables
$p_0,...,p_{N-1}$ that can indicate which polarized channels should carry
frozen bits. Based on this, we present an efficient method to jointly optimize
a puncturing pattern and an information set. Focusing on a fixed information
set, we show that there exist the so-called {\em catastrophic} puncturing
patterns that will surely lead to a block error and derive their weight
distributions recursively. We then propose the two construction methods of a
rate-compatible (RC) polar code which ensures that each puncturing pattern in
the family is non-catastrophic. Simulation results demonstrate that the
proposed RC polar code outperform the RC Turbo code adopted in LTE.

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The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn