Related papers: Folding, Tiling, and Multidimensional Coding
Lattice sieving in two or more dimensions has proven to be an indispensable practical aid in integer factorization and discrete log computations involving the number field sieve. The main contribution of this article is to show that a…
This document describes a convention for compressing n-dimensional images and storing the resulting byte stream in a variable-length column in a FITS binary table. The FITS file structure outlined here is independent of the specific data…
This paper proposes a new class of multi-dimensional nonsystematic Reed-Solomon codes that are constructed based on the multi-dimensional Fourier transform over a finite field. The proposed codes are the extension of the nonsystematic…
Can active forces be exploited to drive the consistent collapse of an active polymer into a folded structure? In this paper we introduce and perform numerical simulations of a simple model of active colloidal folders, and show that a…
We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties of the sequence of finite words obtained by coding a typical…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
This work addresses the question of achieving capacity with lattice codes in multi-antenna block fading channels when the number of fading blocks tends to infinity. In contrast to the standard approach in the literature which employs random…
Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…
We define a metric on $\mathbb{F}_q^n$ using the linear complexity of finite sequences. We will then develop a coding theory for this metric. We will give a Singleton-like bound and we will give constructions of subspaces of…
Coded computation is a method to mitigate "stragglers" in distributed computing systems through the use of error correction coding that has lately received significant attention. First used in vector-matrix multiplication, the range of…
Coded caching scheme provides us an effective framework to realize additional coded multicasting gain by exploiting coding into multiple transmitted signals. The goal of coded caching design is to jointly optimize the placement and delivery…
In recent years, network coding has become one of the most interesting fields and has attracted considerable attention from both industry and academia. The idea of network coding is based on the concept of allowing intermediate nodes to…
We study multiple tilings of 3-dimensional Euclidean space by a convex body. In a multiple tiling, a convex body $P$ is translated with a discrete multiset $\Lambda$ in such a way that each point of the space gets covered exactly $k$ times,…
Three-dimensional (3D) printing's accessibility enables rapid manufacturing but also poses security risks, such as the unauthorized production of untraceable firearms and prohibited items. To ensure traceability and accountability,…
In this manuscript we study properties of multidimensional shifts. More precisely, we study the necessary and sufficient conditions for a shift to be sofic, i.e. the boundary between sofic shifts and effective ones. To this end, we use…
Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series.…
Robotic cloth manipulation faces challenges due to the fabric's complex dynamics and the high dimensionality of configuration spaces. Previous methods have largely focused on isolated smoothing or folding tasks and overly reliant on…
This paper is about the tiling dynamical systems approach to the study of aperiodic order. We compare and contrast four related types of systems: ordinary (one-dimensional) symbolic systems, one-dimensional tiling systems, multidimensional…
In this paper, we analyze $m$-dimensional ($m$D) convolutional codes with finite support, viewed as a natural generalization of one-dimensional (1D) convolutional codes to higher dimensions. An $m$D convolutional code with finite support…
Coded caching is a technique that generalizes conventional caching and promises significant reductions in traffic over caching networks. However, the basic coded caching scheme requires that each file hosted in the server be partitioned…