Exponential Golomb code

The Golomb exponential code of order k is a universal code parameterized by the integer k . Designed by Solomon Golomb . To encode a non-negative number into an exponential Golomb code of order k, you can use the following method:

1. Take the number N in binary, without the last k digits. Add 1 to it (arithmetic): N = N + 1 . Record received N.
2. Count the number of C bits in N.
3. Subtract from C unit: C = C-1 . Write C zero bits before the selected number N.

For order k = 0, the code looks like this:

  0 => 1 => 1
 1 => 10 => 010
 2 => 11 => 011
 3 => 100 => 00100
 4 => 101 => 00101
 5 => 110 => 00110
 6 => 111 => 00111
 7 => 1000 => 0001000
 8 => 1001 => 0001001
 ...

The exponential Golomb code at k = 0 is used in the H.264 and MPEG-4 AVC video compression standards , in which it is also possible to encode signed numbers by assigning the value 0 to the '0' keyword in binary form and the subsequent assignment of code words to increasing input values amplitudes and variable signs.

The Golomb Exponential Code is also used in the Dirac uncompressed video encoding algorithm.

For k = 0, the Golomb exponential coding coincides with the Elias gamma code of the same number plus one. Thus, it can encode zero, while Elias's gamma code can encode only numbers greater than zero.

Despite its close name, Golomb exponential coding is only slightly similar to Golomb coding , which is a type of entropy coding but not a universal code.