17,722 research outputs found
Achieving Secrecy Capacity of the Gaussian Wiretap Channel with Polar Lattices
In this work, an explicit wiretap coding scheme based on polar lattices is
proposed to achieve the secrecy capacity of the additive white Gaussian noise
(AWGN) wiretap channel. Firstly, polar lattices are used to construct
secrecy-good lattices for the mod- Gaussian wiretap channel. Then we
propose an explicit shaping scheme to remove this mod- front end and
extend polar lattices to the genuine Gaussian wiretap channel. The shaping
technique is based on the lattice Gaussian distribution, which leads to a
binary asymmetric channel at each level for the multilevel lattice codes. By
employing the asymmetric polar coding technique, we construct an AWGN-good
lattice and a secrecy-good lattice with optimal shaping simultaneously. As a
result, the encoding complexity for the sender and the decoding complexity for
the legitimate receiver are both O(N logN log(logN)). The proposed scheme is
proven to be semantically secure.Comment: Submitted to IEEE Trans. Information Theory, revised. This is the
authors' own version of the pape
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 for any fixed target error
probability.Comment: full version of the paper to appear in IEEE Trans. Communication
Gauge choices and Entanglement Entropy of two dimensional lattice gauge fields
In this paper, we explore the question of how different gauge choices in a
gauge theory affect the tensor product structure of the Hilbert space in
configuration space. In particular, we study the Coulomb gauge and observe that
the naive gauge potential degrees of freedom cease to be local operators as
soon as we impose the Dirac brackets. We construct new local set of operators
and compute the entanglement entropy according to this algebra in
dimensions. We find that our proposal would lead to an entanglement entropy
that behave very similar to a single scalar degree of freedom if we do not
include further centers, but approaches that of a gauge field if we include
non-trivial centers. We explore also the situation where the gauge field is
Higgsed, and construct a local operator algebra that again requires some
deformation. This should give us some insight into interpreting the
entanglement entropy in generic gauge theories and perhaps also in
gravitational theories.Comment: 38 pages,25 figure
Revisiting Entanglement Entropy of Lattice Gauge Theories
Casini et al raise the issue that the entanglement entropy in gauge theories
is ambiguous because its definition depends on the choice of the boundary
between two regions.; even a small change in the boundary could annihilate the
otherwise finite topological entanglement entropy between two regions. In this
article, we first show that the topological entanglement entropy in the Kitaev
model which is not a true gauge theory, is free of ambiguity. Then, we give a
physical interpretation, from the perspectives of what can be measured in an
experiement, to the purported ambiguity of true gauge theories, where the
topological entanglement arises as redundancy in counting the degrees of
freedom along the boundary separating two regions. We generalize these
discussions to non-Abelian gauge theories.Comment: 15 pages, 3 figure
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