Related papers: Linear-Equation Ordered-Statistics Decoding
Training Neural Ordinary Differential Equations (ODEs) is often computationally expensive. Indeed, computing the forward pass of such models involves solving an ODE which can become arbitrarily complex during training. Recent works have…
Error estimating coding (EEC) is a standard technique for estimating the number of bit errors during packet transmission over wireless networks. In this paper, we propose OddEEC, a novel EEC scheme. OddEEC is a nontrivial adaptation of a…
Despite the NP hardness of acquiring minimum distance $d_m$ for linear codes theoretically, in this paper we propose one experimental method of finding minimum-weight codewords, the weight of which is equal to $d_m$ for LDPC codes. One…
The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
We study a problem of constructing codes that transform a channel with high bit error rate (BER) into one with low BER (at the expense of rate). Our focus is on obtaining codes with smooth ("graceful") input-output BER curves (as opposed to…
This paper considers sparse linear discriminant analysis of high-dimensional data. In contrast to the existing methods which are based on separate estimation of the precision matrix $\O$ and the difference $\de$ of the mean vectors, we…
In this paper, the paradigm of sphere decoding (SD) for solving the integer least square problem (ILS) is revisited, where extra degrees of freedom are introduced to exploit the decoding potential. Firstly, the equivalent sphere decoding…
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…
In this paper, we study the tradeoffs between complexity and reliability for decoding large linear block codes. We show that using artificial neural networks to predict the required order of an ordered statistics based decoder helps in…
Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…
Code embeddings capture the semantic representations of code and are crucial for various code-related large language model (LLM) applications, such as code search. Previous training primarily relies on optimizing the InfoNCE loss by…
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…
This paper proposes the use of spectral element methods \citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary Differential Equations (ODE-Nets; \citealp{Chen2018NeuralOD}) for system identification. This is achieved…
This study investigates the problem of learning linear block codes optimized for Belief-Propagation decoders significantly improving performance compared to the state-of-the-art. Our previous research is extended with an enhanced system…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue…
In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or…
Ordinary differential equations (ODEs) are widely used to describe the time evolution of natural phenomena across various scientific fields. Estimating the parameters of these systems from data is a challenging task, particularly when…