3,759 research outputs found
Dual-lattice ordering and partial lattice reduction for SIC-based MIMO detection
This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, we propose low-complexity lattice detection algorithms for successive interference cancelation (SIC) in multi-input multi-output (MIMO) communications. First, we present a dual-lattice view of the vertical Bell Labs Layered Space-Time (V-BLAST) detection. We show that V-BLAST ordering is equivalent to applying sorted QR decomposition to the dual basis, or equivalently, applying sorted Cholesky decomposition to the associated Gram matrix. This new view results in lower detection complexity and allows simultaneous ordering and detection. Second, we propose a partial reduction algorithm that only performs lattice reduction for the last several, weak substreams, whose implementation is also facilitated by the dual-lattice view. By tuning the block size of the partial reduction (hence the complexity), it can achieve a variable diversity order, hence offering a graceful tradeoff between performance and complexity for SIC-based MIMO detection. Numerical results are presented to compare the computational costs and to verify the achieved diversity order
On the Proximity Factors of Lattice Reduction-Aided Decoding
Lattice reduction-aided decoding features reduced decoding complexity and
near-optimum performance in multi-input multi-output communications. In this
paper, a quantitative analysis of lattice reduction-aided decoding is
presented. To this aim, the proximity factors are defined to measure the
worst-case losses in distances relative to closest point search (in an infinite
lattice). Upper bounds on the proximity factors are derived, which are
functions of the dimension of the lattice alone. The study is then extended
to the dual-basis reduction. It is found that the bounds for dual basis
reduction may be smaller. Reasonably good bounds are derived in many cases. The
constant bounds on proximity factors not only imply the same diversity order in
fading channels, but also relate the error probabilities of (infinite) lattice
decoding and lattice reduction-aided decoding.Comment: remove redundant figure
Linearizing torsion classes in the Picard group of algebraic curves over finite fields
We address the problem of computing in the group of -torsion rational
points of the jacobian variety of algebraic curves over finite fields, with a
view toward computing modular representations.Comment: To appear in Journal of Algebr
On the Geometric Ergodicity of Metropolis-Hastings Algorithms for Lattice Gaussian Sampling
Sampling from the lattice Gaussian distribution is emerging as an important
problem in coding and cryptography. In this paper, the classic
Metropolis-Hastings (MH) algorithm from Markov chain Monte Carlo (MCMC) methods
is adapted for lattice Gaussian sampling. Two MH-based algorithms are proposed,
which overcome the restriction suffered by the default Klein's algorithm. The
first one, referred to as the independent Metropolis-Hastings-Klein (MHK)
algorithm, tries to establish a Markov chain through an independent proposal
distribution. We show that the Markov chain arising from the independent MHK
algorithm is uniformly ergodic, namely, it converges to the stationary
distribution exponentially fast regardless of the initial state. Moreover, the
rate of convergence is explicitly calculated in terms of the theta series,
leading to a predictable mixing time. In order to further exploit the
convergence potential, a symmetric Metropolis-Klein (SMK) algorithm is
proposed. It is proven that the Markov chain induced by the SMK algorithm is
geometrically ergodic, where a reasonable selection of the initial state is
capable to enhance the convergence performance.Comment: Submitted to IEEE Transactions on Information Theor
Decoding by Sampling: A Randomized Lattice Algorithm for Bounded Distance Decoding
Despite its reduced complexity, lattice reduction-aided decoding exhibits a
widening gap to maximum-likelihood (ML) performance as the dimension increases.
To improve its performance, this paper presents randomized lattice decoding
based on Klein's sampling technique, which is a randomized version of Babai's
nearest plane algorithm (i.e., successive interference cancelation (SIC)). To
find the closest lattice point, Klein's algorithm is used to sample some
lattice points and the closest among those samples is chosen. Lattice reduction
increases the probability of finding the closest lattice point, and only needs
to be run once during pre-processing. Further, the sampling can operate very
efficiently in parallel. The technical contribution of this paper is two-fold:
we analyze and optimize the decoding radius of sampling decoding resulting in
better error performance than Klein's original algorithm, and propose a very
efficient implementation of random rounding. Of particular interest is that a
fixed gain in the decoding radius compared to Babai's decoding can be achieved
at polynomial complexity. The proposed decoder is useful for moderate
dimensions where sphere decoding becomes computationally intensive, while
lattice reduction-aided decoding starts to suffer considerable loss. Simulation
results demonstrate near-ML performance is achieved by a moderate number of
samples, even if the dimension is as high as 32
SAWdoubler: a program for counting self-avoiding walks
This article presents SAWdoubler, a package for counting the total number
Z(N) of self-avoiding walks (SAWs) on a regular lattice by the length-doubling
method, of which the basic concept has been published previously by us. We
discuss an algorithm for the creation of all SAWs of length N, efficient
storage of these SAWs in a tree data structure, and an algorithm for the
computation of correction terms to the count Z(2N) for SAWs of double length,
removing all combinations of two intersecting single-length SAWs.
We present an efficient numbering of the lattice sites that enables
exploitation of symmetry and leads to a smaller tree data structure; this
numbering is by increasing Euclidean distance from the origin of the lattice.
Furthermore, we show how the computation can be parallelised by distributing
the iterations of the main loop of the algorithm over the cores of a multicore
architecture. Experimental results on the 3D cubic lattice demonstrate that
Z(28) can be computed on a dual-core PC in only 1 hour and 40 minutes, with a
speedup of 1.56 compared to the single-core computation and with a gain by
using symmetry of a factor of 26. We present results for memory use and show
how the computation is made to fit in 4 Gbyte RAM. It is easy to extend the
SAWdoubler software to other lattices; it is publicly available under the GNU
LGPL license.Comment: 29 pages, 3 figure
On products and powers of linear codes under componentwise multiplication
In this text we develop the formalism of products and powers of linear codes
under componentwise multiplication. As an expanded version of the author's talk
at AGCT-14, focus is put mostly on basic properties and descriptive statements
that could otherwise probably not fit in a regular research paper. On the other
hand, more advanced results and applications are only quickly mentioned with
references to the literature. We also point out a few open problems.
Our presentation alternates between two points of view, which the theory
intertwines in an essential way: that of combinatorial coding, and that of
algebraic geometry.
In appendices that can be read independently, we investigate topics in
multilinear algebra over finite fields, notably we establish a criterion for a
symmetric multilinear map to admit a symmetric algorithm, or equivalently, for
a symmetric tensor to decompose as a sum of elementary symmetric tensors.Comment: 75 pages; expanded version of a talk at AGCT-14 (Luminy), to appear
in vol. 637 of Contemporary Math., AMS, Apr. 2015; v3: minor typos corrected
in the final "open questions" sectio
- âŠ