Capacity-approaching codes | Coding theory

Fountain code

In coding theory, fountain codes (also known as rateless erasure codes) are a class of erasure codes with the property that a potentially limitless sequence of encoding symbols can be generated from a given set of source symbols such that the original source symbols can ideally be recovered from any subset of the encoding symbols of size equal to or only slightly larger than the number of source symbols. The term fountain or rateless refers to the fact that these codes do not exhibit a fixed code rate. A fountain code is optimal if the original k source symbols can be recovered from any k successfully received encoding symbols (i.e., excluding those that were erased). Fountain codes are known that have efficient encoding and decoding algorithms and that allow the recovery of the original k source symbols from any kโ€™ of the encoding symbols with high probability, where kโ€™ is just slightly larger than k. LT codes were the first practical realization of fountain codes. Raptor codes and online codes were subsequently introduced, and achieve linear time encoding and decoding complexity through a pre-coding stage of the input symbols. (Wikipedia).

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What is the definition of scientific notation

๐Ÿ‘‰ Learn about scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the number of digits up to t

From playlist Scientific Notation | Learn About

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How to use decimal points

๐Ÿ‘‰ Learn all about decimals. Decimals are numbers written with a decimal point. Digits can be written to the right or to the left of the decimal point. Digits are written to the left of the decimal point increase in value by multiples of 10 while digits written to the right decrease by mul

From playlist Decimals | Learn About

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Understanding Matrices and Matrix Notation

In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start

From playlist Mathematics (All Of It)

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Learn how to identify if a function is a polynomial and identify the degree and LC

๐Ÿ‘‰ Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

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How to convert a number from scientific notation to a decimal

๐Ÿ‘‰ Learn how to convert numbers from scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the nu

From playlist How to Convert Scientific Notation to a Number

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Learn how to write a number our from scientific notation

๐Ÿ‘‰ Learn how to convert numbers from scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the nu

From playlist How to Convert Scientific Notation to a Number

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๐Ÿ‘‰ Learn how to multiply numbers written in scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is

From playlist Scientific Notation

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Classify a polynomial then determining if it is a polynomial or not

๐Ÿ‘‰ Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

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How to write a number from scientific notation as a whole number

๐Ÿ‘‰ Learn how to convert numbers from scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the nu

From playlist How to Convert Scientific Notation to a Number

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This Drill Powered Spool Proves Me Right

Start speaking a new language in 3 weeks with Babbel. Get up to 65% OFF your subscription here: https://go.babbel.com/12m65-youtube-stevemould-aug-2021/default This is my response to Mehdi's video on the chain fountain, aka The Mould Effect. Check out Mehdi's channel ElectroBOOM here: ht

From playlist Chain fountain playlist

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A 2D Heron's Fountain Behaves Weirdly

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From playlist Best of

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The REAL REASON for Chain Fountain, BONUS: Ocean Clean up #TeamSeas

Iโ€™m sure there wonโ€™t be any further discussions after I make my point on the Mould Effect and how the chain fountain works! If you like my argument, then donate to the fundraiser or go to https://TeamSeas.org and help clean up the oceans! All Chain Fountain Dispute Videos: Steveโ€™s Last Vi

From playlist Everything in chronological order

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GED 'Most Missed' Math Practice Problems , Code Q.4.b, #3

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! The GED Testing Service keeps a list of the most missed math topics and can be seen here: http://www.gedtestingservice.com/uploads/files/126de0283c94ff6323b3b5

From playlist GED 'Most Missed' Sample Questions

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World Record Chain Fountain? The Mould Effect Explained

Get your first month of KiwiCo free: https://kiwico.com/stevemould I attempt to to make the tallest Chain Fountain (otherwise known as the Mould Effect). I also explain the science behind why the fountain rises. See Mehdi's video here: https://youtu.be/hx2LEqTQT4E See my original chain f

From playlist Experiments

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Locally symmetric spaces: pp-adic aspects - Laurent Fargues

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From playlist Mathematics

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GED 'Most Missed' Math Practice Problems , Code Q.4.b, #2

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! The GED Testing Service keeps a list of the most missed math topics and can be seen here: http://www.gedtestingservice.com/uploads/files/126de0283c94ff6323b3b5

From playlist GED 'Most Missed' Sample Questions

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How to write a number in scientific notation as a whole number

๐Ÿ‘‰ Learn how to convert numbers from scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the nu

From playlist How to Convert Scientific Notation to a Number

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Statistical Learning: 10.R.2 Convolutional Neural Networks in R

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Raptor code | Megabyte | Linear network coding | Reliable multicast | Online codes | Coding theory | Code rate | Sequence | Coupon collector's problem | Secret sharing | Algorithm | Analysis of algorithms | Systematic code