Huffman Coding

Huffman coding is a lossless data compression technique based on the statistics of the appearance of characters in the message.

Huffman assigns binary codes of variable length to the different characters according to their frequency of appearance in the message to be compressed (the most frequent benefiting from a short code in order to reduce the total size of the data).

The Huffman code calculates the frequency of appearance of letters in the text, and sort the characters from the most frequent to the least frequent.

The Huffman algorithm will create a tree with leaves as the found letters and for value (or weight) their number of occurrences in the message. To create this tree, look for the 2 weakest nodes (smaller weight) and hook them to a new node whose weight is the sum of the 2 nodes. Repeat the process until having only one node, which will become the root (and that will have as weight the total number of letters of the message).

The binary code of each character is then obtained by browsing the tree from the root to the leaves and noting the path (0 or 1) to each node. The set of character-binary associations constitutes the dictionary.

Decryption of the Huffman code requires knowledge of the matching tree or dictionary (characters <-> binary codes)

To decrypt, browse the tree from root to leaves (usually top to bottom) until you get an existing leaf (or a known value in the dictionary).

By applying the algorithm of the Huffman coding, the most frequent characters (with greater occurrence) are coded with the smaller binary words, thus, the size used to code them is minimal, which increases the compression.

The compression ratio often exceeds 50%, especially if the message is long and made up mostly of the same characters.

However, Huffman does not work well with small data sizes, because the overhead of the tree representation can negate the compression gains.

The encoded message is in binary format (or in a hexadecimal representation) and must be accompanied by a correspondence tree/dictionary table for decryption.

The presence of variable length codes is an important feature.

The notions of a tree, tree structure or pruning (technique aiming to optimize the tree by dynamically removing branches/nodes) are clues.

The tree/dictionary is needed to correctly assign codes to symbols. Without it, decryption becomes complicated or even impossible.

By making assumptions about the length of the message and the size of the binary words, it is possible to search for the probable list of words used by Huffman.

It should then be associated with the right letters, which represents a second difficulty for decryption and certainly requires automatic methods.

There are variants of Huffman when creating the tree / dictionary.

The dictionary can be static: each character / byte has a predefined code and is known or published in advance (so it does not need to be transmitted)

The dictionary can be semi-adaptive: the content is analyzed to calculate the frequency of each character and an optimized tree is used for encoding (it must then be transmitted for decoding). This is the version implemented on dCode

The dictionary can be adaptive: from a known tree (published before and therefore not transmitted) it is modified during compression and optimized as and when. The calculation time is much longer but often offers a better compression ratio.

Morse code uses variable length codes similar to Huffman coding.

It was published in 1952 by David Albert Huffman.