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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).
Adaptive Huffman coding (also called Dynamic Huffman coding) is an adaptive coding technique based on Huffman coding. It permits building the code as the symbols are being transmitted, having no initial knowledge of source distribution, that allows one-pass encoding and adaptation to changing conditions in data.
The package-merge algorithm is an O(nL)-time algorithm for finding an optimal length-limited Huffman code for a given distribution on a given alphabet of size n, where no code word is longer than L. It is a greedy algorithm , and a generalization of Huffman's original algorithm .
The standard way to represent a signal made of 4 symbols is by using 2 bits/symbol, but the entropy of the source is 1.73 bits/symbol. If this Huffman code is used to represent the signal, then the entropy is lowered to 1.83 bits/symbol; it is still far from the theoretical limit because the probabilities of the symbols are different from negative powers of two.
Modified Huffman coding is used in fax machines to encode black-on-white images . It combines the variable-length codes of Huffman coding with the coding of repetitive data in run-length encoding . The basic Huffman coding provides a way to compress files with much repeating data, like a file containing text, where the alphabet letters are the ...
The normal Huffman coding algorithm assigns a variable length code to every symbol in the alphabet. More frequently used symbols will be assigned a shorter code. For example, suppose we have the following non-canonical codebook: A = 11 B = 0 C = 101 D = 100 Here the letter A has been assigned 2 bits, B has 1 bit, and C and D both have 3 bits.
For this reason, Shannon–Fano codes are almost never used; Huffman coding is almost as computationally simple and produces prefix codes that always achieve the lowest possible expected code word length, under the constraints that each symbol is represented by a code formed of an integral number of bits. This is a constraint that is often ...
Such an approach allows simpler and faster encoding/decoding than arithmetic coding or even Huffman coding, since the latter requires a table lookups. In the {0.95, 0.05} example, a Golomb-Rice code with a four-bit remainder achieves a compression ratio of 71.1 % {\displaystyle 71.1\%} , far closer to optimum than using three-bit blocks.