相关论文: Permutation Polynomial Interleavers: An Algebraic-…
The variation in the prescribed modulation schemes and code rates for WiMAX interleaver design, as defined by IEEE 802.16 standard, demands a plethora of hardware if all the modulation schemes and code rates have to be unified into a single…
We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the…
We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…
In this paper we introduce the class of Spread Codes for the use in random network coding. Spread Codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding…
Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In recent works of the authors the…
Log-concave distributions are an attractive choice for modeling and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions and thus is a rich and flexible…
This dissertation considers new constructions and decoding approaches for error-correcting codes based on non-conventional polynomials, with the objective of providing new coding solutions to the applications mentioned above. With skew…
We introduce a new velocity selection criterion for fronts propagating into unstable and metastable states. We restrict these fronts to large finite intervals in the comoving frame of reference and require their centers be insensitive to…
A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin-Kasteleyn random…
In a wireless storage system, having to communicate over a fading channel makes repair transmissions prone to physical layer errors. The first approach to combat fading is to utilize the existing optimal space-time codes. However, it was…
We report on the design of an all-mirror wavefront-division interferometer capable of spectroscopic studies across multiple spectral ranges$\unicode{x2013}$from the plasma frequencies of metals to terahertz wavelengths and beyond. The…
We modify the pre-factor of the semiclassical propagator to improve its efficiency in practical implementations. The new pre-factor represents the smooth portion of an orbit's contribution, and leads to fast convergence in numerical…
Polymers in nonuniform flows undergo strong deformation, which in the presence of persistent stretching can result in the coil-stretch transition. This phenomenon has been characterized by using the formalism of nonequilibrium statistical…
Estimating the shape of an elliptical distribution is a fundamental problem in statistics. One estimator for the shape matrix, Tyler's M-estimator, has been shown to have many appealing asymptotic properties. It performs well in numerical…
Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing…
A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the…
The Temperley-Lieb algebra \tln(\beta) can be defined as the set of rectangular diagrams with n points on each of their vertical sides, with all points joined pairwise by non-intersecting strings. The multiplication is then the…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
We present the theory of linear rank-metric codes from the point of view of their fundamental parameters. These are: the minimum rank distance, the rank distribution, the maximum rank, the covering radius, and the field size. The focus of…
In this paper we investigate the structure of the fundamental polytope used in the Linear Programming decoding introduced by Feldman, Karger and Wainwright. We begin by showing that for expander codes, every fractional pseudocodeword always…