Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\beta$-expansion: A Theoretical Framework for Fast and Recursive
  Construction of Polar Codes   In this work, we introduce $\beta$-expansion, a notion borrowed from number
theory, as a theoretical framework to study fast construction of polar codes
based on a recursive structure of universal partial order (UPO) and
polarization weight (PW) algorithm. We show that polar codes can be recursively
constructed from UPO by continuously solving several polynomial equations at
each recursive step. From these polynomial equations, we can extract an
interval for $\beta$, such that ranking the synthetic channels through a
closed-form $\beta$-expansion preserves the property of nested frozen sets,
which is a desired feature for low-complex construction. In an example of AWGN
channels, we show that this interval for $\beta$ converges to a constant close
to $1.1892 \approx 2^{1/4}$ when the code block-length trends to infinity. Both
asymptotic analysis and simulation results validate our theoretical claims.

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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat