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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).
A Huffman code is a variable-length string of bits that identifies a unique token. A Huffman-threaded interpreter locates subroutines using an index table or a tree of pointers that can be navigated by the Huffman code. Huffman-threaded code is one of the most compact representations known for a computer program. The index and codes are chosen ...
The optimal length-limited Huffman code will encode symbol i with a bit string of length h i. The canonical Huffman code can easily be constructed by a simple bottom-up greedy method, given that the h i are known, and this can be the basis for fast data compression. [2]
Here the letter A has been assigned 2 bits, B has 1 bit, and C and D both have 3 bits. To make the code a canonical Huffman code, the codes are renumbered. The bit lengths stay the same with the code book being sorted first by codeword length and secondly by alphabetical value of the letter: B = 0 A = 11 C = 101 D = 100
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 [1] [2] but in most mathematical books and articles (e.g ...
The two codes (the 288-symbol length/literal tree and the 32-symbol distance tree) are themselves encoded as canonical Huffman codes by giving the bit length of the code for each symbol. The bit lengths are themselves run-length encoded to produce as compact a representation as possible.
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 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.