Related papers: Techniques in Lattice Basis Reduction
Over the last years, novel low-complexity approaches to the equalization of MIMO channels have gained much attention. Thereby, methods based on lattice basis reduction are of special interest, as they achieve the optimum diversity order. In…
Since the invention of the famous LLL algorithm, lattice reduction has been an extremely useful tool in computational number theory. By construction, the LLL algorithm deals with lattices living in a vector space endowed with a positive…
A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. Some of the famous lattice reduction…
Multiple-input multiple-output (MIMO) systems are playing an important role in the recent wireless communication. The complexity of the different systems models challenge different researches to get a good complexity to performance balance.…
Lattices are a popular field of study in mathematical research, but also in more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In mathematical theory, most often lattices over real numbers are…
This paper introduces a heuristic topology optimization framework for thin-walled, 2D extruded lattice structures subject to complex high-speed loading. The proposed framework optimizes the wall thickness distribution in the lattice cross…
Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape…
A simple scheme for communication over MIMO broadcast channels is introduced which adopts the lattice reduction technique to improve the naive channel inversion method. Lattice basis reduction helps us to reduce the average transmitted…
DeepLLL algorithm (Schnorr, 1994) is a famous variant of LLL lattice basis reduction algorithm, and PotLLL algorithm (Fontein et al., 2014) and $S^2$LLL algorithm (Yasuda and Yamaguchi, 2019) are recent polynomial-time variants of DeepLLL…
The integration of Large Language Models (LLMs) into optimization has created a powerful synergy, opening exciting research opportunities. This paper investigates how LLMs can enhance existing optimization algorithms. Using their…
Lattices defined as modules over algebraic rings or orders have garnered interest recently, particularly in the fields of cryptography and coding theory. Whilst there exist many attempts to generalise the conditions for LLL reduction to…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
This work presents a novel lattice-based methodology for incorporating multidimensional constraints into continuous decision variables within a genetic algorithm (GA) framework. The proposed approach consolidates established transcription…
A new architecture called integer-forcing (IF) linear receiver has been recently proposed for multiple-input multiple-output (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be…
The machine learning of lattice operators has three possible bottlenecks. From a statistical standpoint, it is necessary to design a constrained class of operators based on prior information with low bias, and low complexity relative to the…
For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a provably deterministic polynomial-time algorithm to accomplish…
We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the $L_1$-penalized regression (lasso) in the literature, but it seems to have…
A novel Lattice Boltzmann method is derived using the Principle of Minimum Cross Entropy (MinxEnt) via the minimization of Kullback-Leibler Divergence (KLD). By carrying out the actual single step Newton-Raphson minimization (MinxEnt-LBM) a…
Lattice gas algorithms (LGA) are a class of algorithms including, in chronological order, binary lattice gas cellular automata (LGCA), integer lattice gas algorithms (ILGA) and lattice Boltzmann method (LBM). They are largely used for…
Clustering is a fundamental primitive in unsupervised learning which gives rise to a rich class of computationally-challenging inference tasks. In this work, we focus on the canonical task of clustering d-dimensional Gaussian mixtures with…