Prefix code

Coding theory

A prefix code is a type of code system distinguished by its possession of the "prefix property", which requires that there is no whole code word in the system that is a prefix (initial segment) of any other code word in the system. It is trivially true for fixed-length code, so only a point of consideration in variable-length code. For example, a code with code words {9, 55} has the prefix property; a code consisting of {9, 5, 59, 55} does not, because "5" is a prefix of "59" and also of "55". A prefix code is a uniquely decodable code: given a complete and accurate sequence, a receiver can identify each word without requiring a special marker between words. However, there are uniquely decodable codes that are not prefix codes; for instance, the reverse of a prefix code is still uniquely decodable (it is a suffix code), but it is not necessarily a prefix code. Prefix codes are also known as prefix-free codes, prefix condition codes and instantaneous codes. Although Huffman coding is just one of many algorithms for deriving prefix codes, prefix codes are also widely referred to as "Huffman codes", even when the code was not produced by a Huffman algorithm. The term comma-free code is sometimes also applied as a synonym for prefix-free codes but in most mathematical books and articles (e.g.) a comma-free code is used to mean a self-synchronizing code, a subclass of prefix codes. Using prefix codes, a message can be transmitted as a sequence of concatenated code words, without any out-of-band markers or (alternatively) special markers between words to frame the words in the message. The recipient can decode the message unambiguously, by repeatedly finding and removing sequences that form valid code words. This is not generally possible with codes that lack the prefix property, for example {0, 1, 10, 11}: a receiver reading a "1" at the start of a code word would not know whether that was the complete code word "1", or merely the prefix of the code word "10" or "11"; so the string "10" could be interpreted either as a single codeword or as the concatenation of the words "1" then "0". The variable-length Huffman codes, country calling codes, the country and publisher parts of ISBNs, the Secondary Synchronization Codes used in the UMTS W-CDMA 3G Wireless Standard, and the instruction sets (machine language) of most computer microarchitectures are prefix codes. Prefix codes are not error-correcting codes. In practice, a message might first be compressed with a prefix code, and then encoded again with channel coding (including error correction) before transmission. For any uniquely decodable code there is a prefix code that has the same code word lengths. Kraft's inequality characterizes the sets of code word lengths that are possible in a uniquely decodable code. (Wikipedia).

(IC 2.6) Prefix codes - remarks and what's next

Definition of a prefix code (a.k.a. prefix-free code a.k.a. instantaneous code) for lossless compression. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

Is your name also a NUMBER? | Find what number your name is with math and code

In base-36, the number 360927794919225 is expressed using the numeral deeplizard. Yes. Everyone's name is also a number in some base. Let's check this out. Notebook links: https://beta.observablehq.com/@deeplizard/positional-numeral-systems https://beta.observablehq.com/@deeplizard/find-

From playlist Data Science - Learn to code for beginners

Types Of Numbers | Numbers | Maths | FuseSchool

We all know what numbers are 1, 2, 3, 4, 5, …. Including negative numbers -1, -2, -3, -4, -5, ... But did you know that mathematicians classify numbers into different types… into a number system. Let’s start at the top with real numbers. They can be positive… negative… zero… decimals, frac

From playlist MATHS: Numbers

(IC 2.5) Prefix codes

From playlist Information theory and Coding

How to use decimal points

👉 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

Learn how to write a number our from scientific notation

👉 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

5 Patterns with Numbers - Binary to Base-36 | Numerals across bases

What numeral is used to express the number 17 in base-16. a) 17 b) 1 c) 11 d) 2 Soon you'll be able to snap answer questions like this one for any base. This is due to one of the patterns I'm about show you for numeral systems. Let's check it out. Notebook: https://beta.observablehq.com

From playlist Data Science - Learn to code for beginners

1,010,010,101,000,011 - #MegaFavNumbers

This is my submission to the #megafavnumbers project. My number is 1010010101000011, which is prime in bases 2, 3, 4, 5, 6 and 10. I've open-sourced my code: https://bitbucket.org/Bip901/multibase-primes Clarification: by "ignoring 1" I mean ignoring base 1, since this number cannot be fo

From playlist MegaFavNumbers

(IC 4.7) Optimality of Huffman codes (part 2) - weak siblings

We prove that Huffman codes are optimal. In part 2, we show that there exists an optimal prefix code with a pair of "weak siblings". A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

(IC 4.13) Not every optimal prefix code is Huffman

Every Huffman code is an optimal prefix code, but the converse is not true. This is illustrated with an example. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

Python Programming Practice: LeetCode #14 -- Longest Common Prefix

In this episode of Python Programming Practice, we tackle LeetCode #14 -- Longest Common Prefix. Link to the problem here: https://leetcode.com/problems/longest-common-prefix/ If you don't know Python, you can learn the basics of Python for data analysis using this guide I created on Kag

From playlist Python Programming Practice

(IC 5.4) Why the interval needs to be completely contained

To ensure unique decodeability, it's necessary that the interval [a,b) contain the whole interval corresponding to the encoded binary sequence, rather than just containing the number corresponding to the binary sequence. A playlist of these videos is available at: http://www.youtube.com/

From playlist Information theory and Coding

1. Unsigned Binary Numbers - How to Convert From Unsigned Binary Numbers to Whole Numbers

This tutorial shows how to convert from an unsigned binary number to a whole number. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)

From playlist Binary Numbers

Lec 2 | MIT 6.450 Principles of Digital Communications I, Fall 2006

Lecture 2: Discrete source encoding View the complete course at: http://ocw.mit.edu/6-450F06 Instructors: Prof. Lizhong Zheng, Prof. Robert Gallager License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.450 Principles of Digital Communications, I Fall 2006

(IC 2.10) Kraft-McMillan - examples for (b)

For a given set of lengths, the Kraft-McMillan inequality is a necessary condition for the existence of a uniquely decodable code, and a sufficient condition for the existence of a prefix code. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC83

From playlist Information theory and Coding

Nexus Trimester - Moni Naor (Wezimann Institute of Science)

How to Share a Secret, Infinitely Moni Naor (Wezimann Institute of Science) March 31, 2016 Abstract: Secret sharing schemes allow a dealer to distribute a secret piece of information among several parties such that only qualified subsets of parties can reconstruct the secret. The collecti

From playlist Nexus Trimester - 2016 - Secrecy and Privacy Theme

(IC 2.11) Kraft-McMillan - proof sketch for (b)

From playlist Information theory and Coding

Numeral vs Number | Introducing numeral systems for programming beginners

What's the difference between the number 12 and the numeral 12? A numeral system is any writing system that allows us to express numbers using symbols. When we express a number using symbols, the result is called a numeral. When we express a number using a numeral, numeral is said to enc

From playlist Data Science - Learn to code for beginners

Prefix code

Related pages