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Truncated binary encoding is an entropy encoding typically used for uniform probability distributions with a finite alphabet. It is parameterized by an alphabet with total size of number n . It is a slightly more general form of binary encoding when n is not a power of two .
Golomb coding is a lossless data compression method using a family of data compression codes invented by Solomon W. Golomb in the 1960s. Alphabets following a geometric distribution will have a Golomb code as an optimal prefix code, [1] making Golomb coding highly suitable for situations in which the occurrence of small values in the input stream is significantly more likely than large values.
Truncated binary encoding is a straightforward generalization of fixed-length codes to deal with cases where the number of symbols n is not a power of two. Source symbols are assigned codewords of length k and k+1, where k is chosen so that 2 k < n ≤ 2 k+1.
Unary coding, [nb 1] or the unary numeral system and also sometimes called thermometer code, is an entropy encoding that represents a natural number, n, with a code of length n + 1 ( or n), usually n ones followed by a zero (if natural number is understood as non-negative integer) or with n − 1 ones followed by a zero (if natural number is understood as strictly positive integer).
The modern binary number system, the basis for binary code, is an invention by Gottfried Leibniz in 1689 and appears in his article Explication de l'Arithmétique Binaire (English: Explanation of the Binary Arithmetic) which uses only the characters 1 and 0, and some remarks on its usefulness. Leibniz's system uses 0 and 1, like the modern ...
In the base −2 representation, a signed number is represented using a number system with base −2. In conventional binary number systems, the base, or radix, is 2; thus the rightmost bit represents 2 0, the next bit represents 2 1, the next bit 2 2, and so on. However, a binary number system with base −2 is also possible.
The binary-reflected Gray code list for n bits can be generated recursively from the list for n − 1 bits by reflecting the list (i.e. listing the entries in reverse order), prefixing the entries in the original list with a binary 0, prefixing the entries in the reflected list with a binary 1, and then concatenating the original list with the ...
This encoding method leverages the fact that subtracting the remainder from a dividend results in a multiple of the divisor. Hence, if we take our message polynomial p ( x ) {\displaystyle p(x)} as before and multiply it by x n − k {\displaystyle x^{n-k}} (to "shift" the message out of the way of the remainder), we can then use Euclidean ...