Editing Golomb coding (section)

== Adaptive run-length Golomb–Rice encoding ==

When a probability distribution for integers is not known, the optimal parameter for a Golomb–Rice encoder cannot be determined. Thus, in many applications, a two-pass approach is used: first, the block of data is scanned to estimate a probability density function (PDF) for the data. The Golomb–Rice parameter is then determined from that estimated PDF. A simpler variation of that approach is to assume that the PDF belongs to a parametrized family, estimate the PDF parameters from the data, and then compute the optimal Golomb–Rice parameter. That is the approach used in most of the applications discussed below.

An alternative approach to efficiently encode integer data whose PDF is not known, or is varying, is to use a backwards-adaptive encoder. The RLGR encoder [https://www.microsoft.com/en-us/research/publication/adaptive-run-length-golomb-rice-encoding-of-quantized-generalized-gaussian-sources-with-unknown-statistics/] achieves that using a very simple algorithm that adjusts the Golomb–Rice parameter up or down, depending on the last encoded symbol. A decoder can follow the same rule to track the variation of the encoding parameters, so no side information needs to be transmitted, just the encoded data. Assuming a generalized Gaussian PDF, which covers a wide range of statistics seen in data such as prediction errors or transform coefficients in multimedia codecs, the RLGR encoding algorithm can perform very well in such applications.