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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).
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]
In order for a symbol code scheme such as the Huffman code to be decompressed, the same model that the encoding algorithm used to compress the source data must be provided to the decoding algorithm so that it can use it to decompress the encoded data. In standard Huffman coding this model takes the form of a tree of variable-length codes, with ...
Run-length encoding in the previous step is designed to take care of codes that have an inverse probability of use higher than the shortest code Huffman code in use. If multiple Huffman tables are in use, the selection of each table (numbered 0 to 5) is done from a list by a zero-terminated bit run between 1 and 6 bits in length.
Huffman threaded code consists of lists of tokens stored as Huffman codes. 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 ...
In the table below is an example of creating a code scheme for symbols a 1 to a 6. The value of l i gives the number of bits used to represent the symbol a i . The last column is the bit code of each symbol.
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. As an alternative to including the tree representation ...
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 ...