Related papers: Linear-Equation Ordered-Statistics Decoding
Information set decoding (ISD) algorithms are the best known procedures to solve the decoding problem for general linear codes. These algorithms are hence used for codes without a visible structure, or for which efficient decoders…
New algorithms for efficient decoding of polar codes (which may be CRC-augmented), transmitted over either a binary erasure channel (BEC) or an additive white Gaussian noise channel (AWGNC), are presented. We start by presenting a new…
We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory)…
This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least…
Sphere decoding (SD) of polar codes is an efficient method to achieve the error performance of maximum likelihood (ML) decoding. But the complexity of the conventional sphere decoder is still high, where the candidates in a target sphere…
In this paper, we propose a fast decoder algorithm for uniquely decodable (errorless) code sets for overloaded synchronous optical code-division multiple-access (O-CDMA) systems. The proposed decoder is designed in a such a way that the…
Efficient and scalable decoding of quantum codes is essential for high-performance quantum error correction. In this work, we introduce Reliable Subset Reduction (RSR), a reliability-driven preprocessing framework that leverages belief…
The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of…
In this paper, we propose a pre-configured error pattern ordered statistics decoding (PEPOSD) algorithm and discuss its application to short cyclic redundancy check (CRC)-polar codes. Unlike the traditional OSD that changes the most…
The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…
We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery…
We introduce a novel universal soft-decision decoding algorithm for binary block codes called ordered reliability direct error pattern testing (ORDEPT). Our results, obtained for a variety of popular short high-rate codes, demonstrate that…
LP-type problems such as the Minimum Enclosing Ball (MEB), Linear Support Vector Machine (SVM), Linear Programming (LP), and Semidefinite Programming (SDP) are fundamental combinatorial optimization problems, with many important…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…