Related papers: An Approximation of Theta Functions with Applicati…
We demonstrate a decoding scheme for nested lattice codes which is able to decode a list of a particular size which contains the transmitted codeword with high probability. This list decoder is analogous to that used in random coding…
Lattice coding techniques may be used to derive achievable rate regions which outperform known independent, identically distributed (i.i.d.) random codes in multi-source relay networks and in particular the two-way relay channel. Gains stem…
A density functional theory (DFT) of lattice fermion models is presented, which uses the single-particle density matrix gamma_{ij} as basic variable. A simple, explicit approximation to the interaction-energy functional W[gamma] of the…
The nearest lattice point problem in $\mathbb{R}^n$ is formulated in a distributed network with $n$ nodes. The objective is to minimize the probability that an incorrect lattice point is found, subject to a constraint on inter-node…
In this paper, a construction of constant weight codes based on the unique decomposition of elements in lattices is presented. The conditions for unique primary decomposition and unique irreducible decomposition in lattices are discussed…
An important step in the efficient computation of multi-dimensional theta functions is the construction of appropriate symplectic transformations for a given Riemann matrix assuring a rapid convergence of the theta series. An algorithm is…
In this paper, new probability estimates are derived for ideal lattice codes from totally real number fields using ideal class Dedekind zeta functions. In contrast to previous work on the subject, it is not assumed that the ideal in…
A lattice is a set of all the integer linear combinations of certain linearly independent vectors. One of the most important concepts on lattice is the successive minima which is of vital importance from both theoretical and practical…
It is well-known that the densest lattice sphere packings also typically have large kissing numbers. The sphere packing density maximization problem is known to have a solution among well-rounded lattices, of which the integer lattice…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
Low-latency communication is one of the most important application scenarios in next-generation wireless networks. Often in communication-theoretic studies latency is defined as the time required for the transmission of a packet over a…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…
A lattice decoder which represents messages explicitly as a mixture of Gaussians functions is given. In order to prevent the number of functions in a mixture from growing as the decoder iterations progress, a method for replacing N Gaussian…
We consider the minimization of theta functions $\theta\_\Lambda(\alpha)=\sum\_{p\in\Lambda}e^{-\pi\alpha|p|^2}$ amongst lattices $\Lambda\subset \mathbb R^d$, by reducing the dimension of the problem, following as a motivation the case…
In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated through a small set of smooth functions. The invariance is either by translations under a…
Reliable and low latency multicast communication is important for future vehicular communication. Sparse random linear network coding approach used to ensure the reliability of multicast communication has been widely investigated. A…
The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. As near capacity-approaching codes, Low-Density Parity-Check (LDPC) codes possess several advantages over…
Lattices are an efficient and effective method to encode ambiguity of upstream systems in natural language processing tasks, for example to compactly capture multiple speech recognition hypotheses, or to represent multiple linguistic…
In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface. The modified near…