Golomb coding

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, 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.

Rice coding (invented by Robert F. Rice) denotes using a subset of the family of Golomb codes to produce a simpler (but possibly suboptimal) prefix code. Rice used this set of codes in an adaptive coding scheme; "Rice coding" can refer either to that adaptive scheme or to using that subset of Golomb codes. Whereas a Golomb code has a tunable parameter that can be any positive integer value, Rice codes are those in which the tunable parameter is a power of two. This makes Rice codes convenient for use on a computer since multiplication and division by 2 can be implemented more efficiently in binary arithmetic.

Rice coding is used as the entropy encoding stage in a number of lossless image compression and audio data compression methods.

Golomb coding uses a tunable parameter ${\displaystyle M}$ to divide an input value ${\displaystyle N}$ into two parts: ${\displaystyle q}$, the result of a division by ${\displaystyle M}$, and ${\displaystyle r}$, the remainder. The quotient is sent in unary coding, followed by the remainder in truncated binary encoding. When ${\displaystyle M=1}$ Golomb coding is equivalent to unary coding.

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