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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.
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).
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.
Huffman coding and arithmetic coding (when they can be used) give at least as good, and often better compression than any universal code. However, universal codes are useful when Huffman coding cannot be used — for example, when one does not know the exact probability of each message, but only knows the rankings of their probabilities.
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.
If symbols are assigned in ranges of lengths being powers of 2, we would get Huffman coding. For example, a->0, b->100, c->101, d->11 prefix code would be obtained for tANS with "aaaabcdd" symbol assignment. Example of generation of tANS tables for m = 3 size alphabet and L = 16 states, then applying them for stream decoding.
Arithmetic coding achieves compression rates close to the best possible for a particular statistical model, which is given by the information entropy, whereas Huffman compression is simpler and faster but produces poor results for models that deal with symbol probabilities close to 1.
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 ...