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Let $S(A)$ denote the orbit of a complex or real matrix $A$ under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the…

Numerical Analysis · Mathematics 2013-01-07 C. K. Li , Y. T. Poon , T. Schulte-Herbrueggen

Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…

Quantum Algebra · Mathematics 2024-04-09 Hao Shi , Guofeng Zhang , Ming Zhang

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as massive MIMO, where there are hundreds of antennas at one side of the link. Motivated by the fact…

Information Theory · Computer Science 2015-06-18 Nafiseh Shariati , Emil Björnson , Mats Bengtsson , Mérouane Debbah

This paper presents an efficient quadratic programming (QP) decoder via the alternating direction method of multipliers (ADMM) technique, called QP-ADMM, for binary low-density parity-check (LDPC) codes. Its main contents are as follows:…

Information Theory · Computer Science 2020-02-19 Jing Bai , Yongchao Wang , Qingjiang Shi

The least-mean-squares (LMS) algorithm is the most popular algorithm in adaptive filtering. Several variable step-size strategies have been suggested to improve the performance of the LMS algorithm. These strategies enhance the performance…

Data Structures and Algorithms · Computer Science 2017-03-22 Muhammad Omer Bin Saeed

With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…

Chemical Physics · Physics 2020-04-03 William Dawson , Stephan Mohr , Laura E. Ratcliff , Takahito Nakajima , Luigi Genovese

Quantum low-density parity check (qLDPC) codes offer higher encoding rate than topological codes, e.g. surface codes, making them favourable for practical, fault-tolerant quantum computing with low overhead. These codes are particularly…

Quantum Physics · Physics 2025-09-23 Susan X. Chen , Matthias C. Löbl , Ming Lai Chan , Anders S. Sørensen , Stefano Paesani

A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSC) is proposed. Based on the enumeration of the smallest weight error…

Information Theory · Computer Science 2007-07-13 Hua Xiao , Amir H. Banihashemi

Due to dependence between codeword elements, index modulation (IM) and related modulation techniques struggle to provide simple solutions for practical problems such as Gray coding between information bits and constellation points; and…

Information Theory · Computer Science 2022-01-21 Ferhat Yarkin , Justin P. Coon

In this paper, we propose a learning-based block-wise planar channel estimator (LBPCE) with high accuracy and low complexity to estimate the time-varying frequency-selective channel of a multiple-input multiple-output (MIMO) orthogonal…

Signal Processing · Electrical Eng. & Systems 2024-05-21 Chenchen Liu , Wenjun Jiang , Xiaojun Yuan

This paper introduces a new approach for the computation of electromagnetic field derivatives, up to any order, with respect to the material and geometric parameters of a given geometry, in a single Finite-Difference Time-Domain (FDTD)…

Numerical Analysis · Mathematics 2024-12-20 Kae-An Liu , Hans-Dieter Lang , Costas D. Sarris

In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random…

Numerical Analysis · Mathematics 2018-04-03 Ivan G. Graham , Frances Y. Kuo , Dirk Nuyens , Rob Scheichl , Ian H. Sloan

Bit-flipping (BF) decoding of low-density parity-check codes is of low complexity but gives inferior performance in general. To improve performance and provide new BF decoder options for complexity-performance tradeoffs, we propose new…

Information Theory · Computer Science 2015-09-01 Tofar C. -Y. Chang , Yu T. Su

We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…

Numerical Analysis · Mathematics 2024-04-05 Christian Alber , Chupeng Ma , Robert Scheichl

Affine frequency division multiplexing (AFDM) has recently emerged as an excellent backward-compatible 6G waveform. In this paper, we study matched filtering (MF) assisted channel estimation (CE) for AFDM systems in complex doubly selective…

Signal Processing · Electrical Eng. & Systems 2026-02-18 Xiangjun Li , Zilong Liu , Zhengchun Zhou , Pingzhi Fan

We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…

Numerical Analysis · Mathematics 2024-12-12 Anastasia Istratuca , Aretha Teckentrup

To achieve reliable and efficient transmissions in free-space optical (FSO) communication, this paper designs a new protograph low-density parity-check (PLDPC) coded generalized spatial multipulse position modulation (GSMPPM) system over…

Information Theory · Computer Science 2023-03-08 Liang Lv , Yi Fang , Lin Dai , Yonghui Li , Mohsen Guizani

Given a lowpass filter, finding a dual lowpass filter is an essential step in constructing non-redundant wavelet filter banks. Obtaining dual lowpass filters is not an easy task. In this paper, we introduce a new method called committee…

Numerical Analysis · Mathematics 2012-01-10 Youngmi Hur

In this paper, we present a fast min-sum algorithm for decoding LDPC codes over GF(q). Our algorithm is different from the one presented by David Declercq and Marc Fossorier in ISIT 05 only at the way of speeding up the horizontal scan in…

Information Theory · Computer Science 2016-11-15 Xiaofei Huang , Suquan Ding , Zhixing Yang , Youshou Wu

Algorithms for minimal enclosing ball problems are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus here on a particularly simple geodesic-based method. A recent subgradient-based study…

Optimization and Control · Mathematics 2026-04-08 Ariel Goodwin , Adrian S. Lewis