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In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression.The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".
Finally, there is a list of items, each of which is a 1 dollar coin or a package consisting of two or more smaller coins whose denominations total 1 dollar. They are also sorted in order of numismatic value. The coin collector then selects the least value N of them. Note that the time of the algorithm is linear in the number of coins.
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
[1] 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 ...
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 ...
Suppose we want to encode the message "AABA<EOM>", where <EOM> is the end-of-message symbol. For this example it is assumed that the decoder knows that we intend to encode exactly five symbols in the base 10 number system (allowing for 10 5 different combinations of symbols with the range [0, 100000)) using the probability distribution {A: .60; B: .20; <EOM>: .20}.
Huffman coding is an entropy encoding method and variable-length code algorithm that assigns more common values with shorter binary codes that require fewer bits to store. Huffman coding works in the context of silence compression by assigning frequently occurring silence patterns with shorter binary codes, reducing data size. [5] [6]
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.
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