Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of Capacity-Achieving Lattice Codes: Polar Lattices   In this paper, we propose a new class of lattices constructed from polar
codes, namely polar lattices, to achieve the capacity $\frac{1}{2}\log(1+\SNR)$
of the additive white Gaussian-noise (AWGN) channel. Our construction follows
the multilevel approach of Forney \textit{et al.}, where we construct a
capacity-achieving polar code on each level. The component polar codes are
shown to be naturally nested, thereby fulfilling the requirement of the
multilevel lattice construction. We prove that polar lattices are
\emph{AWGN-good}. Furthermore, using the technique of source polarization, we
propose discrete Gaussian shaping over the polar lattice to satisfy the power
constraint. Both the construction and shaping are explicit, and the overall
complexity of encoding and decoding is $O(N\log N)$ for any fixed target error
probability.

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int