Coding theory | Error detection and correction

Zemor's decoding algorithm

In coding theory, Zemor's algorithm, designed and developed by Gilles Zemor, is a recursive low-complexity approach to code construction. It is an improvement over the algorithm of Sipser and Spielman. Zemor considered a typical class of Sipser–Spielman construction of expander codes, where the underlying graph is bipartite graph. Sipser and Spielman introduced a constructive family of asymptotically good linear-error codes together with a simple parallel algorithm that will always remove a constant fraction of errors. The article is based on Dr. Venkatesan Guruswami's course notes (Wikipedia).

Zemor's decoding algorithm
Video thumbnail

Dimitri Zvonkine - Hurwitz numbers, the ELSV formula, and the topological recursion

We will use the example of Hurwitz numbers to make an introduction into the intersection theory of moduli spaces of curves and into the subject of topological recursion.

From playlist ­­­­Physique mathématique des nombres de Hurwitz pour débutants

Video thumbnail

Graeffe's Method

Graeffe's Root-Squaring Method (also called Graeffe-Dandelin-Lobachevskiĭ or Dandelin–Lobachesky–Graeffe method) for finding roots of polynomials. The method solves for all of the roots of a polynomial by only using the coefficients and does not require derivatives nor an interation funct

From playlist Root Finding

Video thumbnail

Dimitri Zvonkine - On two ELSV formulas

The ELSV formula (discovered by Ekedahl, Lando, Shapiro and Vainshtein) is an equality between two numbers. The first one is a Hurwitz number that can be defined as the number of factorizations of a given permutation into transpositions. The second is the integral of a characteristic class

From playlist 4th Itzykson Colloquium - Moduli Spaces and Quantum Curves

Video thumbnail

Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - A.Harrow

Aram Harrow (MIT) / 15.09.17 Title: Local Hamiltonians Whose Ground States are Hard to Approximate Abstract: Ground states of local Hamiltonians are typically highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entan

From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

Video thumbnail

Iteration

Powered by https://www.numerise.com/ Iteration

From playlist Numerical Methods

Video thumbnail

Solve a System of Equations by Using Elimination of Multiplying

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

Video thumbnail

Ramanujan Graphs and Siran Graphs, Applications to Quantum Coding Theory - Jean-Pierre Tillich

Jean-Pierre Tillich INRIA, France March 16, 2012 We explain in this talk how Ramanujan graphs can be used to devise optimal cycle codes and review how other graph families related to a construction proposed by Margulis yield interesting families of quantum codes with logarithmic minimum di

From playlist Mathematics

Video thumbnail

Yves Meyer - The 2017 Abel Prize Laureate

Shortfilm about Yves Meyer made by Ekaterina Eremenko/ EEFilms

From playlist Yves Meyer

Video thumbnail

Using a Multiplier to Solve the System of Equations Using Elimination

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

Video thumbnail

Algorithmizing the Multiplicity Schwartz-Zippel Lemma - Prahladh Harsha

Computer Science/Discrete Mathematics Seminar I Topic: Algorithmizing the Multiplicity Schwartz-Zippel Lemma Speaker: Prahladh Harsha Affiliation: Tata Institute of Fundamental Research Date: January 31, 2022 The degree mantra states that any non-zero univariate polynomial of degree at

From playlist Mathematics

Video thumbnail

Using two multipliers when solving a system of equations using the addition method

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Hard

Video thumbnail

(IC 5.14) Finite-precision arithmetic coding - Decoder

Pseudocode for the arithmetic coding decoder, using finite-precision. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

Video thumbnail

(IC 5.7) Decoder for arithmetic coding (infinite-precision)

Pseudocode for the arithmetic coding algorithm, assuming addition and multiplication can be done exactly (i.e. with infinite precision). Later we modify this to work with finite precision. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

Video thumbnail

Solve Linear Equation with Fractions Two Ways y/5+y/2=3/4

This video explains how to solve a linear equation with fraction two different ways.

From playlist Solving Multi-Step Equations

Video thumbnail

Lec 20 | MIT 6.451 Principles of Digital Communication II, Spring 2005

The Sum-Product Algorithm View the complete course: http://ocw.mit.edu/6-451S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.451 Principles of Digital Communication II

Video thumbnail

Using a multiplier with one equation to use the add method to solve the system of equation

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

Video thumbnail

Local Correctability of Expander Codes - Brett Hemenway

Brett Hemenway University of Pennsylvania April 14, 2014 An error-correcting code is called locally decodable if there exists a decoding algorithm that can recover any symbol of the message with high probability by reading only a small number of symbols of the corrupted codeword. There is

From playlist Mathematics

Video thumbnail

List decoding with double samplers - Inbal Livni-Navon

Computer Science/Discrete Mathematics Seminar I Topic: List decoding with double samplers Speaker: Inbal Livni-Navon Affiliation: Weizmann Institute Date: December 6, 2021 The ABNNR encoding is a classical encoding scheme that amplifies the distance of an error correcting code. The enco

From playlist Mathematics

Video thumbnail

Xavier Bresson: "The Transformer Network for the Traveling Salesman Problem"

Deep Learning and Combinatorial Optimization 2021 "The Transformer Network for the Traveling Salesman Problem" Xavier Bresson - Nanyang Technological University, Singapore Abstract: The Traveling Salesman Problem (TSP) is the most popular and most studied combinatorial problem, starting

From playlist Deep Learning and Combinatorial Optimization 2021

Video thumbnail

Using Elimination and the LCM to Solve a System

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

Related pages

Adjacency matrix | Coding theory | Bipartite graph | Geometric series | Finite field | Tanner graph | Ramanujan graph | Expander code