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This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given…

Information Theory · Computer Science 2026-01-15 Henrique K. Miyamoto , Sheng Yang

This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…

Optimization and Control · Mathematics 2012-05-30 Joseph W. Norman

This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial linear systems and we assume that errors can occur in the…

Symbolic Computation · Computer Science 2021-02-09 Guerrini Eleonora , Lebreton Romain , Zappatore Ilaria

This paper is concerned with list decoding of $2$-interleaved binary alternant codes. The principle of the proposed algorithm is based on a combination of a list decoding algorithm for (interleaved) Reed-Solomon codes and an algorithm for…

Information Theory · Computer Science 2022-02-14 Chih-Chiang Huang , Hedongliang Liu , Lukas Holzbaur , Sven Puchinger , Antonia Wachter-Zeh

Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of…

Numerical Analysis · Mathematics 2025-10-20 Grigori Litvinov

In this paper we present a decoding algorithm for algebraic geometry codes with error-correcting capacity beyond half the designed distance of the code. This algorithm comes as a fusion of the Power Error Locating Pairs algorithm for…

Information Theory · Computer Science 2021-03-24 Isabella Panaccione

Finite alphabet iterative decoders (FAIDs) for LDPC codes were recently shown to be capable of surpassing the Belief Propagation (BP) decoder in the error floor region on the Binary Symmetric channel (BSC). More recently, the technique of…

Information Theory · Computer Science 2012-07-20 Shiva Kumar Planjery , Bane Vasic , David Declercq

Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…

Numerical Analysis · Mathematics 2020-12-14 Alec Michael Dunton , Alyson Fox

An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…

Information Theory · Computer Science 2021-11-17 Nir Weinberger

In an error-correcting code, a sender encodes a message $x \in \{ 0, 1 \}^k$ such that it is still decodable by a receiver on the other end of a noisy channel. In the setting of \emph{error-correcting codes with feedback}, after sending…

Information Theory · Computer Science 2024-10-04 Meghal Gupta , Rachel Yun Zhang

The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be…

Quantum Physics · Physics 2016-05-09 Joseph M. Renes

We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…

Quantum Physics · Physics 2012-10-26 Zachary W. E. Evans , Ashley M. Stephens

Constructing Reed-Solomon (RS) codes that can correct insertion and deletion (ins-del) errors has been the focus of several recent studies. However, efficient decoding algorithms for such codes have received less attention and remain a…

Information Theory · Computer Science 2025-07-02 Shubhransh Singhvi

Modern spacecraft communication systems rely on concatenated error correction schemes, typically combining convolutional and Reed-Solomon (RS) codes. This paper presents a decoder-side method that uses a machine learning model to estimate…

Information Theory · Computer Science 2025-09-12 Michael Greenwood , Robert Hunter

In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…

Information Theory · Computer Science 2009-08-06 K. Prasad , B. Sundar Rajan

In this paper we present an effective coarse space correction addressed to accelerate the solution of an algebraic linear system. The system arises from the formulation of the problem of interpolating scattered data by means of Radial Basis…

Numerical Analysis · Mathematics 2019-12-10 Guillaume Gbikpi-Benissan , Frederic Magoules

A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…

Optimization and Control · Mathematics 2020-02-27 V. Peiris , N. Sharon , N. Sukhorukova J. Ugon

We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…

Numerical Analysis · Mathematics 2008-07-10 Joerg Kampen

This paper considers the multi-parametric linear complementarity problem (pLCP) with sufficient matrices. The main result is an algorithm to find a polyhedral decomposition of the set of feasible parameters and to construct a piecewise…

Optimization and Control · Mathematics 2008-07-16 Sebastiano Columbano , Komei Fukuda , Colin Jones

The paper considers recovery of signals from incomplete observations and a problem of determination of the allowed quantity of missed observations, i.e. the problem of determination of the size of the uniqueness sets for a given data…

Information Theory · Computer Science 2022-07-20 Nikolai Dokuchaev