Canonical Huffman code

Coding theory

In computer science and information theory, a canonical Huffman code is a particular type of Huffman code with unique properties which allow it to be described in a very compact manner. Data compressors generally work in one of two ways. Either the decompressor can infer what codebook the compressor has used from previous context, or the compressor must tell the decompressor what the codebook is. Since a canonical Huffman codebook can be stored especially efficiently, most compressors start by generating a "normal" Huffman codebook, and then convert it to canonical Huffman before using it. In order for a scheme such as the Huffman code to be decompressed, the same model that the encoding algorithm used to compress the source data must be provided to the decoding algorithm so that it can use it to decompress the encoded data. In standard Huffman coding this model takes the form of a tree of variable-length codes, with the most frequent symbols located at the top of the structure and being represented by the fewest bits. However, this code tree introduces two critical inefficiencies into an implementation of the coding scheme. Firstly, each node of the tree must store either references to its child nodes or the symbol that it represents. This is expensive in memory usage and if there is a high proportion of unique symbols in the source data then the size of the code tree can account for a significant amount of the overall encoded data. Secondly, traversing the tree is computationally costly, since it requires the algorithm to jump randomly through the structure in memory as each bit in the encoded data is read in. Canonical Huffman codes address these two issues by generating the codes in a clear standardized format; all the codes for a given length are assigned their values sequentially. This means that instead of storing the structure of the code tree for decompression only the lengths of the codes are required, reducing the size of the encoded data. Additionally, because the codes are sequential, the decoding algorithm can be dramatically simplified so that it is computationally efficient. (Wikipedia).

(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

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From playlist Information theory and Coding

(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 4.12) Optimality of Huffman codes (part 7) - existence

We prove that Huffman codes are optimal. In part 7, we show that there exists an optimal code for any given p. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

Huffman Encoding! (Day 3)

And we finally got huffman encoding working with Julia. Some minor changes to be made still. -- Watch live at https://www.twitch.tv/simuleios

From playlist Huffman forest

(IC 4.8) Optimality of Huffman codes (part 3) - sibling codes

We prove that Huffman codes are optimal. In part 3, we show that there exists a "sibling code". A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

Huffman Encoding! (Day 4)

Well, we floundered around today (as usual). Got the decoder working, though. That was nice. -- Watch live at https://www.twitch.tv/simuleios

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Huffman Encoding (Day 1)

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Huffman Encoding! (Day 5)

Alright, didn't get as far as I wanted, but we got something up and running. -- Watch live at https://www.twitch.tv/simuleios

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Everything You Need to Know About JPEG - Episode 4 Part 1: Huffman Decoding

In this series you will learn all of the in-depth details of the complex and sophisticated JPEG image compression format In this episode, we learn all about Huffman codes, how to create a Huffman Coding Tree, and how to create Huffman codes based on a JPEG Huffman Table Jump into the pla

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(IC 4.6) Optimality of Huffman codes (part 1) - inverse ordering

We prove that Huffman codes are optimal. In part 1, we show that the lengths are inversely ordered with the probabilities. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

Week 8: Wednesday - CS50 2007 - Harvard University

Huffman coding. Preprocessing. Compiling. Assembling. Linking. CPUs. Ant-8.

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Order, Entropy, Information, and Compression (Lecture 2) by Dov Levine

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From playlist Entropy, Information and Order in Soft Matter

Huffman Encoding! (Day 2)

Woo! Spent the whole day learning about priority queues in julia! -- Watch live at https://www.twitch.tv/simuleios

From playlist Huffman forest

Huffman forests -- Day 1

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From playlist Huffman forest

Order, Entropy, Information, and Compression (Lecture 1) by Dov Levine

From playlist Entropy, Information and Order in Soft Matter

(IC 4.10) Optimality of Huffman codes (part 5) - extension lemma

We prove that Huffman codes are optimal. In part 5, we show that the H-extension of an optimal code is optimal. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

(IC 4.11) Optimality of Huffman codes (part 6) - induction

We prove that Huffman codes are optimal. In part 6, we complete the proof by induction. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F

From playlist Information theory and Coding

Canonical Huffman code

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