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Huffman tree generated from the exact frequencies of the text "this is an example of a huffman tree". Encoding the sentence with this code requires 135 (or 147) bits, as opposed to 288 (or 180) bits if 36 characters of 8 (or 5) bits were used (This assumes that the code tree structure is known to the decoder and thus does not need to be counted as part of the transmitted information).
It is an online coding technique based on Huffman coding. Having no initial knowledge of occurrence frequencies, it permits dynamically adjusting the Huffman's tree as data are being transmitted. In a FGK Huffman tree, a special external node, called 0-node, is used to identify a newly coming character. That is, whenever new data is encountered ...
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.
Instructions to generate the necessary Huffman tree immediately follow the block header. The static Huffman option is used for short messages, where the fixed saving gained by omitting the tree outweighs the percentage compression loss due to using a non-optimal (thus, not technically Huffman) code. Compression is achieved through two steps:
More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies [(())] [ (())], where is the number of symbols in a code word, is the coding function, is the number of symbols used to make output codes and is the probability of the source symbol. An entropy coding attempts to ...
In this system, the shape of the Huffman coding tree is described as an Otter tree and encoded as a binary number in the interval from 0 to the Wedderburn–Etherington number for the number of symbols in the code. In this way, the encoding uses a very small number of bits, the base-2 logarithm of the Wedderburn–Etherington number. [12]
Arithmetic coding – Entropy encoding; Burrows–Wheeler transform reversible transform for making textual data more compressible, used by bzip2; Huffman coding – Entropy encoding, pairs well with other algorithms; Lempel-Ziv compression (LZ77 and LZ78) – Dictionary-based algorithm that forms the basis for many other algorithms
In the field of data compression, Shannon coding, named after its creator, Claude Shannon, is a lossless data compression technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured).