相关论文: Ulam Sphere Size Analysis for Permutation and Mult…

Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…

Recent interest on permutation rank modulation shows the Kendall tau metric as an important distance metric. This note documents our first efforts to obtain upper bounds on optimal code sizes (for said metric) ala Delsarte's approach. For…

We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation…

Permutation synchronization is an important problem in computer science that constitutes the key step of many computer vision tasks. The goal is to recover $n$ latent permutations from their noisy and incomplete pairwise measurements. In…

A permutation-invariant code on m qubits is a subspace of the symmetric subspace of the m qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading order spontaneous…

In this work, we introduce Variational Umbrella Seeding, a novel technique for computing nucleation barriers. This new method, a refinement of the original seeding approach, is far less sensitive to the choice of order parameter for…

Sphere packing bounds (SPBs) ---with prefactors that are polynomial in the block length--- are derived for codes on two families of memoryless channels using Augustin's method: (possibly non-stationary) memoryless channels with (possibly…

We developed a polarization modulation unit (PMU) to rotate a waveplate continuously in order to observe solar magnetic fields by spectropolarimetry. The non-uniformity of the PMU rotation may cause errors in the measurement of the degree…

The Ulam distance of two permutations on $[n]$ is $n$ minus the length of their longest common subsequence. In this paper, we show that for every $\varepsilon>0$, there exists some $\alpha>0$, and an infinite set $\Gamma\subseteq…

In recent years, due to the spread of multi-level non-volatile memories (NVM), $q$-ary write-once memories (WOM) codes have been extensively studied. By using WOM codes, it is possible to rewrite NVMs $t$ times before erasing the cells. The…

We have modified a commercial NOR flash memory array to enable high-precision tuning of individual floating-gate cells for analog computing applications. The modified array area per cell in a 180 nm process is about 1.5 um^2. While this…

This paper considers coding for so-called partially stuck memory cells. Such memory cells can only store partial information as some of their levels cannot be used due to, e.g., wear out. First, we present a new code construction for…

We obtain new restrictions on the linear programming bound for sphere packing, by optimizing over spaces of modular forms to produce feasible points in the dual linear program. In contrast to the situation in dimensions 8 and 24, where the…

We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…

Commonly the direct construction and the description of mutually orthogonal Latin squares (MOLS) makes use of difference or quasi-difference matrices. Now there exists a correspondence between MOLS and separable permutation codes. We like…

Limited magnitude asymmetric error model is well suited for flash memory. In this paper, we consider the construction of asymmetric codes correcting single error over $\mathbb{Z}_{2^{k}r}$ and which are based on so called $B_{1}[4](2^{k}r)$…

Convolutional precoding in polarization-adjusted convolutional (PAC) codes can reduce the number of minimum weight codewords (a.k.a error coefficient) of polar codes. This can result in improving the error correction performance of (near)…

Kulkarni and Kiyavash recently introduced a new method to establish upper bounds on the size of deletion-correcting codes. This method is based upon tools from hypergraph theory. The deletion channel is represented by a hypergraph whose…

We propose a novel scheme that allows MIMO system to modulate a set of permutation matrices to send more information bits, extending our initial work on the topic. This system is called Permutation Matrix Modulation (PMM). The basic idea is…

We study linear codes over Gaussian integers equipped with the Mannheim distance. We develop Mannheim-metric analogues of several classical bounds. We derive an explicit formula for the volume of Mannheim balls, which yields a sphere…