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We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…

Information Theory · Computer Science 2019-06-25 Mohammad Vahid Jamali , Mahdi Soleymani , Hessam Mahdavifar

Code-based Distributed Matrix Multiplication (DMM) has been extensively studied in distributed computing for efficiently performing large-scale matrix multiplication using coding theoretic techniques. The communication cost and recovery…

Information Theory · Computer Science 2024-08-06 Jiang Li , Songsong Li , Chaoping Xing

Positive semidefinite programs are an important subclass of semidefinite programs in which all matrices involved in the specification of the problem are positive semidefinite and all scalars involved are non-negative. We present a parallel…

Computational Complexity · Computer Science 2011-04-14 Rahul Jain , Penghui Yao

It is known that the multiplication of an $N \times M$ matrix with an $M \times P$ matrix can be performed using fewer multiplications than what the naive $NMP$ approach suggests. The most famous instance of this is Strassen's algorithm for…

Artificial Intelligence · Computer Science 2023-07-18 Arnaud Deza , Chang Liu , Pashootan Vaezipoor , Elias B. Khalil

Deploying neural networks on edge devices entails a careful balance between the energy required for inference and the accuracy of the resulting classification. One technique for navigating this tradeoff is approximate computing: the process…

Machine Learning · Computer Science 2025-09-18 Morteza Rezaalipour , Francesco Costa , Marco Biasion , Rodrigo Otoni , George A. Constantinides , Laura Pozzi

Polynomial based methods have recently been used in several works for mitigating the effect of stragglers (slow or failed nodes) in distributed matrix computations. For a system with $n$ worker nodes where $s$ can be stragglers, these…

Information Theory · Computer Science 2021-06-10 Aditya Ramamoorthy , Li Tang

In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…

Numerical Analysis · Mathematics 2016-02-11 Yariv Aizenbud , Amir Averbuch

We present algorithms for real and complex dot product and matrix multiplication in arbitrary-precision floating-point and ball arithmetic. A low-overhead dot product is implemented on the level of GMP limb arrays; it is about twice as fast…

Mathematical Software · Computer Science 2024-12-20 Fredrik Johansson

In this paper distributed storage systems with exact repair are studied. A construction for regenerating codes between the minimum storage regenerating (MSR) and the minimum bandwidth regenerating (MBR) points is given. To the best of…

Information Theory · Computer Science 2015-01-21 Toni Ernvall

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a…

Information Theory · Computer Science 2009-10-06 K. V. Rashmi , Nihar B. Shah , P. Vijay Kumar , Kannan Ramchandran

Matrix multiplications between asymmetric bit-width operands, especially between 8- and 4-bit operands are likely to become a fundamental kernel of many important workloads including neural networks and machine learning. While existing SIMD…

Machine Learning · Computer Science 2020-08-04 Dibakar Gope , Jesse Beu , Matthew Mattina

We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement…

Quantum Physics · Physics 2009-11-13 Andrew S. Fletcher , Peter W. Shor , Moe Z. Win

We show that expander codes, when properly instantiated, are high-rate list recoverable codes with linear-time list recovery algorithms. List recoverable codes have been useful recently in constructing efficiently list-decodable codes, as…

Information Theory · Computer Science 2015-03-09 Brett Hemenway , Mary Wootters

Approximate computing is a nascent energy-efficient computing paradigm suitable for error-tolerant applications. However, the value of approximation error depends on the applied inputs where individual output error may reach intolerable…

Emerging Technologies · Computer Science 2019-08-06 Mahmoud Masadeh , Osman Hasan , Sofiene Tahar

We study the bit complexity of inverting diagonally dominant matrices, which are associated with random walk quantities such as hitting times and escape probabilities. Such quantities can be exponentially small, even on undirected…

Data Structures and Algorithms · Computer Science 2025-10-23 Mehrdad Ghadiri , Hoai-An Nguyen , Junzhao Yang

Coded computing is an effective technique to mitigate "stragglers" in large-scale and distributed matrix multiplication. In particular, univariate polynomial codes have been shown to be effective in straggler mitigation by making the…

Information Theory · Computer Science 2021-08-19 Burak Hasircioglu , Jesus Gomez-Vilardebo , Deniz Gunduz

We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show how to construct polynomial schemes for the outer…

Information Theory · Computer Science 2024-05-13 Ryann Cartor , Rafael G. L. D'Oliveira , Salim El Rouayheb , Daniel Heinlein , David Karpuk , Alex Sprintson

In this paper, we propose two new constructions of exact-repair minimum storage regenerating (exact-MBR) codes. Both constructions obtain the encoded symbols by first treating the message vector over GF(q) as a linearized polynomial and…

Information Theory · Computer Science 2013-01-22 Hongmei Xie , Zhiyuan Yan

The rapid updates in error-resilient applications along with their quest for high throughput have motivated designing fast approximate functional units for Field-Programmable Gate Arrays (FPGAs). Studies that proposed imprecise functional…

Hardware Architecture · Computer Science 2022-06-29 Zahra Ebrahimi , Muhammad Zaid , Mark Wijtvliet , Akash Kumar

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. We propose a proximally…

Optimization and Control · Mathematics 2021-03-12 Dmitry Pasechnyuk , Vladislav Matyukhin