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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".
For this reason, Shannon–Fano codes are almost never used; Huffman coding is almost as computationally simple and produces prefix codes that always achieve the lowest possible expected code word length, under the constraints that each symbol is represented by a code formed of an integral number of bits. This is a constraint that is often ...
Arithmetic coding is a more modern coding technique that uses the mathematical calculations of a finite-state machine to produce a string of encoded bits from a series of input data symbols. It can achieve superior compression compared to other techniques such as the better-known Huffman algorithm.
Cryptography or cryptographic coding is the practice and study of techniques for secure communication in the presence of third parties (called adversaries). [8] More generally, it is about constructing and analyzing protocols that block adversaries; [ 9 ] various aspects in information security such as data confidentiality , data integrity ...
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 Each of the existing codes are replaced with a new one of the same length, using the following algorithm:
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 ...
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.
As with a prefix code, the representation of a string as a concatenation of such words is unique. A bifix code is a set of words which is both a prefix and a suffix code. [8] An optimal prefix code is a prefix code with minimal average length. That is, assume an alphabet of n symbols with probabilities () for a prefix code C.