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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).
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 ...
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]
To convolutionally encode data, start with k memory registers, each holding one input bit.Unless otherwise specified, all memory registers start with a value of 0. The encoder has n modulo-2 adders (a modulo 2 adder can be implemented with a single Boolean XOR gate, where the logic is: 0+0 = 0, 0+1 = 1, 1+0 = 1, 1+1 = 0), and n generator polynomials — one for each adder (see figure below).
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 ...
Locally decodable codes are error-correcting codes for which single bits of the message can be probabilistically recovered by only looking at a small (say constant) number of positions of a codeword, even after the codeword has been corrupted at some constant fraction of positions.
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 notation (,,) describes a block code over an alphabet of size , with a block length , message length , and distance . If the block code is a linear block code, then the square brackets in the notation [ n , k , d ] q {\displaystyle [n,k,d]_{q}} are used to represent that fact.