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In information theory, Shannon–Fano–Elias coding is a precursor to arithmetic coding, in which probabilities are used to determine codewords. [1] It is named for Claude Shannon , Robert Fano , and Peter Elias .
In the field of data compression, Shannon coding, named after its creator, Claude Shannon, is a lossless data compression technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured).
Fano's method usually produces encoding with shorter expected lengths than Shannon's method. However, Shannon's method is easier to analyse theoretically. Shannon–Fano coding should not be confused with Shannon–Fano–Elias coding (also known as Elias coding), the precursor to arithmetic coding.
If N = 1, stop; encoding is complete. Prepend the binary representation of N to the beginning of the code. This will be at least two bits, the first bit of which is a 1. Let N equal the number of bits just prepended, minus one. Return to Step 2 to prepend the encoding of the new N. To decode an Elias omega-encoded positive integer:
Shannon–Fano–Elias coding: precursor to arithmetic encoding [5] Entropy coding with known entropy characteristics. Golomb coding: form of entropy coding that is optimal for alphabets following geometric distributions; Rice coding: form of entropy coding that is optimal for alphabets following geometric distributions; Truncated binary encoding
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.
PPM compression implementations vary greatly in other details. The actual symbol selection is usually recorded using arithmetic coding, though it is also possible to use Huffman encoding or even some type of dictionary coding technique. The underlying model used in most PPM algorithms can also be extended to predict multiple symbols.
Articles relating to data compression, the process of encoding information using fewer bits than the original representation. Subcategories This category has the following 9 subcategories, out of 9 total.