837 research outputs found
The DMT classification of real and quaternionic lattice codes
In this paper we consider space-time codes where the code-words are
restricted to either real or quaternion matrices. We prove two separate
diversity-multiplexing gain trade-off (DMT) upper bounds for such codes and
provide a criterion for a lattice code to achieve these upper bounds. We also
point out that lattice codes based on Q-central division algebras satisfy this
optimality criterion. As a corollary this result provides a DMT classification
for all Q-central division algebra codes that are based on standard embeddings.Comment: 6 pages, 1 figure. Conference paper submitted to the International
Symposium on Information Theory 201
Decoding by Embedding: Correct Decoding Radius and DMT Optimality
The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP)
are the core algorithmic problems on Euclidean lattices. They are central to
the applications of lattices in many problems of communications and
cryptography. Kannan's \emph{embedding technique} is a powerful technique for
solving the approximate CVP, yet its remarkable practical performance is not
well understood. In this paper, the embedding technique is analyzed from a
\emph{bounded distance decoding} (BDD) viewpoint. We present two complementary
analyses of the embedding technique: We establish a reduction from BDD to
Hermite SVP (via unique SVP), which can be used along with any Hermite SVP
solver (including, among others, the Lenstra, Lenstra and Lov\'asz (LLL)
algorithm), and show that, in the special case of LLL, it performs at least as
well as Babai's nearest plane algorithm (LLL-aided SIC). The former analysis
helps to explain the folklore practical observation that unique SVP is easier
than standard approximate SVP. It is proven that when the LLL algorithm is
employed, the embedding technique can solve the CVP provided that the noise
norm is smaller than a decoding radius , where
is the minimum distance of the lattice, and . This
substantially improves the previously best known correct decoding bound . Focusing on the applications of BDD to decoding of
multiple-input multiple-output (MIMO) systems, we also prove that BDD of the
regularized lattice is optimal in terms of the diversity-multiplexing gain
tradeoff (DMT), and propose practical variants of embedding decoding which
require no knowledge of the minimum distance of the lattice and/or further
improve the error performance.Comment: To appear in IEEE Transactions on Information Theor
Almost universal codes for fading wiretap channels
We consider a fading wiretap channel model where the transmitter has only
statistical channel state information, and the legitimate receiver and
eavesdropper have perfect channel state information. We propose a sequence of
non-random lattice codes which achieve strong secrecy and semantic security
over ergodic fading channels. The construction is almost universal in the sense
that it achieves the same constant gap to secrecy capacity over Gaussian and
ergodic fading models.Comment: 5 pages, to be submitted to IEEE International Symposium on
Information Theory (ISIT) 201
Strong Coordination with Polar Codes
In this paper, we design explicit codes for strong coordination in two-node
networks. Specifically, we consider a two-node network in which the action
imposed by nature is binary and uniform, and the action to coordinate is
obtained via a symmetric discrete memoryless channel. By observing that polar
codes are useful for channel resolvability over binary symmetric channels, we
prove that nested polar codes achieve a subset of the strong coordination
capacity region, and therefore provide a constructive and low complexity
solution for strong coordination.Comment: 7 pages doublespaced, presented at the 50th Annual Allerton
Conference on Communication, Control and Computing 201
Secret key generation from Gaussian sources using lattice hashing
We propose a simple yet complete lattice-based scheme for secret key
generation from Gaussian sources in the presence of an eavesdropper, and show
that it achieves strong secret key rates up to 1/2 nat from the optimal in the
case of "degraded" source models. The novel ingredient of our scheme is a
lattice-hashing technique, based on the notions of flatness factor and channel
intrinsic randomness. The proposed scheme does not require dithering.Comment: 5 pages, Conference (ISIT 2013
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